diff --git a/readme.md b/readme.md
index df9be4a..1e599b2 100644
--- a/readme.md
+++ b/readme.md
@@ -166,6 +166,15 @@ Simplest functor in javascript is an `Array`
 ```
 ---
 
+## Lift
+
+> Lift takes a function and runs it on values in a container type. Map is a lift over a one-argument function, but the same principal can be used to combine multiple containers of the same type.
+
+```js
+lift(n => n * 2)([2,3,4]); // [4,6,8]
+lift((a, b)  => a * b)([1, 2], [3]); // [3, 6]
+```
+
 ## Referential Transparency
 
 > An expression that can be replaced with its value without changing the
@@ -184,6 +193,8 @@ referential transparent.
 
 ##  Equational Reasoning
 
+> When an application is composed of expressions and devoid of side effects, truths about the system can be derived from the parts.
+
 ---
 
 ## Lazy evaluation
@@ -243,7 +254,7 @@ The identity value is empty array `[]`
 
 ## Monad
 
-> A monad is an abstraction that provides an interface for executing a common sequence of commands on a particular kind of value, often one you want to avoid acting on directly. One of the most common monads is the "maybe" or optional value monad, which wraps a value that could be either nothing or something. By using a monad instead of the raw value, you can protect your code from exposure to null values. Likewise, a "state" monad can be used in a parser to algorithmically consume an input string using a repeatable sequence of steps that preserves the current state of the input from operation to operation. Also, since a monad is, by definition, a special kind of functor that also returns a monad, they can be chained together to describe any sequence of operations. In functional languages with lazy evaluation, monads are used where sequence of evaluation is important, such as in I/O. Due to this sequencing utility, they are sometimes referred to as "programmable semicolons."
+> A monad is a container type that provides two functions, [chain](#chain) and [ap](#applicative-functor). Monads provide an interface for executing a common sequence of commands on a particular kind of value, often one you want to avoid acting on directly. One of the most common monads is the "maybe" or optional value monad, which wraps a value that could be either nothing or something. By using a monad instead of the raw value, you can protect your code from exposure to null values. Likewise, a "state" monad can be used in a parser to algorithmically consume an input string using a repeatable sequence of steps that preserves the current state of the input from operation to operation. Also, since a monad is, by definition, a special kind of functor that also returns a monad, they can be chained together to describe any sequence of operations. In functional languages with lazy evaluation, monads are used where sequence of evaluation is important, such as in I/O. Due to this sequencing utility, they are sometimes referred to as "programmable semicolons."
 
 The simplest monad is the Identity monad. It simply wraps a value.
 
@@ -253,12 +264,28 @@ let Identity = v => ({ bind: transform => transform(v) })
 
 ---
 
+## Chain
+
+> A chain is a container type that implements a chain function. The chain function takes another function to run on the contained value and returns a value in the same container. The passed function must also return a value in the same container. This is also known as bind, or flatmap in other languages.
+
+```js
+['cat,dog','fish,bird'].chain((a) => a.split(',')) // ['cat','dog','fish','bird']
+```
+
+---
+
 ## Comonad
 
 ---
 
 ## Applicative Functor
 
+> An applicative functor is a container type that can have functions put in it. A function often called `ap` is available on the type which applies a function in the container to a value in another container of the same type.
+
+```js
+[(a)=> a + 1].ap([1]) // [2]
+```
+
 ---