diff --git a/source/nix-language/attribute-sets.adoc b/source/nix-language/attribute-sets.adoc
index 1493c0a..da15e52 100644
--- a/source/nix-language/attribute-sets.adoc
+++ b/source/nix-language/attribute-sets.adoc
@@ -1,5 +1,45 @@
 = Attribute set operations
 
+== Selecttion
+
+The `.` operator selects an attribute from a set.
+
+[source]
+....
+nix-repl> animal = { name = { first = "Professor"; last = "Paws"; }; age = 10; species = "cat"; }
+
+nix-repl> animal . age
+10
+
+nix-repl> animal . name . first
+"Professor"
+....
+
+== Query
+
+We can use the `?` operator to find out if a set has a particular attribute.
+
+[source]
+....
+nix-repl> animal ? species
+true
+
+nix-repl> animal ? bicycle
+false
+....
+
+== Modification
+
+We can use the `//` operator to modify an attribute set.
+Recall that Nix values are immutable, so the result is a new value (the original is not modified).
+
+[source]
+....
+nix-repl> animal // { species = "tiger"; }
+{ age = 10; name = { ... }; species = "tiger"; }
+....
+
+== Recursive attribute sets
 
 An ordinary attribute set cannot refer to its own elements.
 To do this, you need a _recursive_ attribute set.
@@ -17,37 +57,3 @@ error: undefined variable 'x'
 nix-repl> rec { x = 3; y = 4*x; }
 { x = 3; y = 12; }
 ....
-
-
-The `.` operator selects an attribute from a set.
-
-[source]
-....
-nix-repl> animal = { name = { first = "Professor"; last = "Paws"; }; age = 10; species = "cat"; }
-
-nix-repl> animal . age
-10
-
-nix-repl> animal . name . first
-"Professor"
-....
-
-We can use the `?` operator to find out if a set has a particular attribute.
-
-[source]
-....
-nix-repl> animal ? species
-true
-
-nix-repl> animal ? bicycle
-false
-....
-
-We can use the `//` operator to modify an attribute set.
-Recall that Nix values are immutable, so the result is a new value (the original is not modified).
-
-[source]
-....
-nix-repl> animal // { species = "tiger"; }
-{ age = 10; name = { ... }; species = "tiger"; }
-....
diff --git a/source/nix-language/booleans.adoc b/source/nix-language/booleans.adoc
index 0a69612..a0c404d 100644
--- a/source/nix-language/booleans.adoc
+++ b/source/nix-language/booleans.adoc
@@ -1,4 +1,4 @@
-# Boolean operations
+= Boolean operations
 
 The usual boolean operators are available.
 Recall that earlier we set `a = 7` and `b = 3`.
diff --git a/source/nix-language/functions.adoc b/source/nix-language/functions.adoc
index fad1d51..3010b7a 100644
--- a/source/nix-language/functions.adoc
+++ b/source/nix-language/functions.adoc
@@ -1,3 +1,123 @@
 = Functions
 
-// TODO
+== Anonymous functions
+
+Functions are defined using the syntax `_parameter_: _expression_`,
+where the _expression_ typically involves the _parameter_.
+Consider the following example.
+
+[source]
+....
+nix-repl> x: x + 1
+«lambda @ «string»:1:1»
+....
+
+We created a function that adds `1` to its input.
+However, it doesn't have a name, so we can't use it directly.
+Anonymous functions do have their uses, as we shall see shortly.
+
+Note that the message printed by the NixREPL when we created the function uses the term _lambda_.
+This derives from a branch of mathematics called _lambda calculus_.
+Lambda calculus was the inspiration for most functional languages such as Nix.
+Functional programmers often call anonymous functions "lambdas".
+
+The Nix REPL confirms that the expression `x: x + 1` defines a function.
+
+[source]
+....
+nix-repl> :t x: x + 1
+a function
+....
+
+== Named functions and function application
+
+How can we use a function?
+Recall from <<type-lambda>> that functions can be treated like any other data type.
+In particular, we can assign it to a variable.
+
+[source]
+....
+nix-repl> f = x: x + 1
+
+nix-repl> f
+«lambda @ «string»:1:2»
+....
+
+Procedural languages such as C or Java often use parenthesis to apply a function to a value, e.g. `f(5)`.
+Nix, like lambda calculus and most functional languages, does not require parenthesis for function application.
+This reduces visual clutter when chaining a series of functions.
+
+Now that our function has a name, we can use it.
+
+[source]
+....
+nix-repl> f 5
+6
+....
+
+== Multiple parameters
+
+Functions in Nix always have a single parameter.
+To define a calculation that requires more than one parameter,
+we create functions that return functions!
+
+[source]
+....
+nix-repl> add = a: (b: a+b)
+....
+
+We have created a function called `add`.
+When applied to a parameter `a`, it returns a new function that adds `a` to its input.
+Note that the expression `(b: a+b)` is an anonymous function.
+We never call it directly, so it doesn't need a name.
+Anonymous functions are useful after all!
+
+[source]
+....
+nix-repl> add 3             # Returns a function that adds 3 to any input
+«lambda @ «string»:1:6»
+....
+
+Now let's apply `add 3` to the value `5`.
+
+[source]
+....
+nix-repl> (add 3) 5
+8
+....
+
+In fact, the parentheses aren't needed.
+
+[source]
+....
+nix-repl> add 3 5
+8
+....
+
+In case that wasn't clear, let's repeat those steps, but in more detail.
+The function `add` takes a single parameter `a`,
+and returns a new function that takes a single parameter `b`, and returns the value `a + b`.
+Let's apply `add` to the value `3`, and give the resulting new function a name, `g`.
+
+[source]
+....
+nix-repl> g = add 3
+....
+
+The function `g` takes a single parameter and adds `3` to it.
+The Nix REPL confirms that `g` is indeed a function.
+
+[source]
+....
+nix-repl> :t g
+a function
+....
+
+Now we can apply `g` to a number to get a new number.
+
+[source]
+....
+nix-repl> g 5
+8
+....
+
diff --git a/source/nix-language/let.adoc b/source/nix-language/let.adoc
index ceff96a..5590fe8 100644
--- a/source/nix-language/let.adoc
+++ b/source/nix-language/let.adoc
@@ -44,3 +44,5 @@ This is similar to how recursive attribute sets work.
 nix-repl> let x = 3; y = x + 1; in x*y
 12
 ....
+
+// TODO Discuss inheriting attributes https://nixos.org/manual/nix/stable/language/constructs#inheriting-attributes
diff --git a/source/nix-language/main.adoc b/source/nix-language/main.adoc
index d59f496..d5bdc67 100644
--- a/source/nix-language/main.adoc
+++ b/source/nix-language/main.adoc
@@ -31,3 +31,5 @@ include::if.adoc[leveloffset=+1]
 include::let.adoc[leveloffset=+1]
 
 include::with.adoc[leveloffset=+1]
+
+// TODO discuss laziness
diff --git a/source/nix-language/numbers.adoc b/source/nix-language/numbers.adoc
index 58a4f70..d44cc91 100644
--- a/source/nix-language/numbers.adoc
+++ b/source/nix-language/numbers.adoc
@@ -1,4 +1,6 @@
-# Numeric operations
+= Numeric operations
+
+== Arithmetic operators
 
 The usual arithmetic operators are provided.
 
@@ -22,8 +24,9 @@ nix-repl> -1      # negation
 
 [IMPORTANT]
 ====
-The spaces before and after operators aren't always required.
-However, you can get unexpected results when you omit them, as shown below.
+As mentioned in <<_variables>>,
+you can get unexpected results when you omit spaces around operators.
+Consider the following example.
 
 [source]
 ....
@@ -37,6 +40,7 @@ Let's use the `:t` command to find out the type of the expression.
 [source]
 ....
 nix-repl> :t 6/2
+a path
 ....
 
 If an expression can be interpreted as a path, Nix will do so.
@@ -55,6 +59,8 @@ nix-repl> 6/ 2
 To avoid surprises and improve readability, I prefer to use spaces before and after all operators.
 ====
 
+== Floating-point calculations
+
 Numbers without a decimal point are assumed to be integers.
 To ensure that a number is interpreted as a floating-point value, add a decimal point.
 
diff --git a/source/nix-language/paths.adoc b/source/nix-language/paths.adoc
index 171dabb..c461574 100644
--- a/source/nix-language/paths.adoc
+++ b/source/nix-language/paths.adoc
@@ -14,7 +14,9 @@ nix-repl> ./.
 /home/amy/codeberg/nix-book
 ....
 
-Paths can be concatenated with each other to produce a new path.
+== Concatenating paths
+
+Paths can be concatenated to produce a new path.
 
 [source]
 ....
@@ -27,8 +29,8 @@ a path
 
 [IMPORTANT]
 ====
-Relative paths become absolute when they are parsed, which occurs before concatenation.
-This is why the result in the example below is not `/home/amy/file.txt`.
+Relative paths are made absolute when they are parsed, which occurs before concatenation.
+This is why the result in the example below is not `/home/wombat/file.txt`.
 
 [source]
 ....
@@ -37,15 +39,16 @@ nix-repl> /home/wombat + ./file.txt
 ....
 ====
 
+== Concatenating a path + a string
 
 A path can be concatenated with a string to produce a new path.
 
 [source]
 ....
-nix-repl> homePath + "/file.txt"
+nix-repl> /home/wombat + "/file.txt"
 /home/wombat/file.txt
 
-nix-repl> :t homePath + "/myfile.txt"
+nix-repl> :t /home/wombat + "/file.txt"
 a path
 ....
 
@@ -56,12 +59,14 @@ String contexts are beyond the scope of this book;
 for more information see https://nixos.org/manual/nix/stable/language/operators#path-concatenation.
 ====
 
+== Concatenating a string + a path
+
 Strings can be concatenated with paths, but with a side-effect that may surprise you:
 if the path exists, the file is copied to the Nix store!
 The result is a string, not a path.
 
 In the example below, the file `file.txt` is copied to `/nix/store/gp8ba25gpwvbqizqfr58jr014gmv1hd8-file.txt`
-(not `/home/wombat/nix/store/gp8ba25gpwvbqizqfr58jr014gmv1hd8-file.txt`).
+(not, as you might expect, to `/home/wombat/nix/store/gp8ba25gpwvbqizqfr58jr014gmv1hd8-file.txt`).
 
 [source]
 ....
diff --git a/source/nix-language/strings.adoc b/source/nix-language/strings.adoc
index 67cc7fb..5e61fe4 100644
--- a/source/nix-language/strings.adoc
+++ b/source/nix-language/strings.adoc
@@ -1,4 +1,6 @@
-# String operations
+= String operations
+
+== String concatenation
 
 String concatenation uses the `+` operator.
 
@@ -8,6 +10,8 @@ nix-repl> "Hello, " + "world!"
 "Hello, world!"
 ....
 
+== String interpolation
+
 You can use the `${_variable_}` syntax to insert the value of a variable within a string.
 
 [source]
@@ -21,7 +25,6 @@ nix-repl> "Hi, I'm ${name}."
 [IMPORTANT]
 ====
 You cannot mix numbers and strings.
-Nix does provide functions for converting between types; we'll see these later.
 Earlier we set `a = 7`, so the following expression fails.
 
 [source]
@@ -37,6 +40,5 @@ error:
 
        error: cannot coerce an integer to a string
 ....
+Nix does provide functions for converting between types; we'll see these in <<_built_in_functions>>.
 ====
-
-// TODO Talk about "strings with context" https://shealevy.com/blog/2018/08/05/understanding-nixs-string-context/
diff --git a/source/nix-language/types.adoc b/source/nix-language/types.adoc
index ed3e5ac..d49bf53 100644
--- a/source/nix-language/types.adoc
+++ b/source/nix-language/types.adoc
@@ -1,5 +1,6 @@
 = Data types
 
+[#type-string]
 == Strings
 
 Strings are enclosed by double quotes (`"`), or _two_ single quotes (`'`).
@@ -15,20 +16,24 @@ They can span multiple lines.
     The sound of water
               -- Basho''
 
+[#type-integer]
 == Integers
 
     7
     256
 
+[#type-float]
 == Floating point numbers
 
     3.14
     6.022e23
 
+[#type-boolean]
 == Boolean
 
 The Boolean values in Nix are `true` and `false`.
 
+[#type-path]
 == Paths
 
 File paths are play an important role in building software, so Nix has a special data type for them.
@@ -40,6 +45,7 @@ listed in the environment variable NIX_PATH to be searched for the given
 file or directory name.
 These are called _lookup paths_.
 
+[#type-list]
 == Lists
 
 List elements are enclosed in square brackets and separated by spaces (not commas).
@@ -55,6 +61,7 @@ List elements can be of any type, and can even be lists themselves.
 
     [ [ 1 2 ] [ 3 4 ] ]
 
+[#type-set]
 == Attribute sets
 
 Attribute sets associate keys with values.
@@ -76,12 +83,15 @@ Values of attribute sets can be of any type, and can even be attribute sets them
 
     { name = { first = "Professor"; last = "Paws"; }; age = 10; species = "cat"; }
 
+In <<_recursive_attribute_sets>> you will be introduced to a special type of attribute set.
+
 [NOTE]
 ====
 In some Nix documentation, and in many articles about Nix,
 attribute sets are simply called "sets".
 ====
 
+[#type-lambda]
 == Functions
 
 We'll learn how to write functions later in this chapter.
diff --git a/source/nix-language/variables.adoc b/source/nix-language/variables.adoc
index fabd304..f140c28 100644
--- a/source/nix-language/variables.adoc
+++ b/source/nix-language/variables.adoc
@@ -1,7 +1,10 @@
 = Variables
 
+// TODO what characters are legal in a variable name/identifier?
+
+== Assignment
+
 You can declare variables in Nix and assign values to them.
-// TODO explain that values are immutable.
 
 [source]
 ....
@@ -15,9 +18,10 @@ nix-repl> a - b
 
 [IMPORTANT]
 ====
-As mentioned previously, omitting the spaces around operators can have unexpected results.
-As Nix allows hyphens (`-`) in variable names,
-`a-b` is interpreted as the name of a variable in the following example.
+The spaces before and after operators aren't always required.
+However, you can get unexpected results when you omit them, as shown in the following example.
+Nix allows hyphens (`-`) in variable names,
+so `a-b` is interpreted as the name of a variable rather than a subtraction operation.
 
 [source]
 ....
@@ -31,3 +35,33 @@ error: undefined variable 'a-b'
 ....
 ====
 
+== Immutability
+
+In Nix, values are _immutable_;
+once you assign a value to a variable, you cannot change it.
+You can, however, create a new variable with the same name, but in a different scope.
+Don't worry if you don't completely understand the previous sentence;
+we will see some examples in <<_functions>>, <<_let_expressions>>, and <<_with_expressions>>.
+
+[IMPORTANT]
+====
+In the Nix REPL, it may seem like the values of variables can be changed,
+in _apparent_ contradiction to the previous paragraph.
+In truth, the REPL works some behind-the-scenes "magic",
+effectively creating a new nested scope with each assignment.
+This makes it much easier to experiment in the REPL.
+
+[source]
+....
+nix-repl> x = 1
+
+nix-repl> x
+1
+
+nix-repl> x = x + 1 # creates a new variable called "x"; the original is no longer in scope
+
+nix-repl> x
+2
+....
+====
+
diff --git a/source/nix-language/with.adoc b/source/nix-language/with.adoc
index 4e97c71..5f93e46 100644
--- a/source/nix-language/with.adoc
+++ b/source/nix-language/with.adoc
@@ -1,4 +1,4 @@
-= With expression
+= With expressions
 
 A `with` expression is somewhat similar to a `let` expression,
 but it brings all of the associations in an attribute set into scope.