diff --git a/README.md b/README.md
index 8867a3a..2313ca2 100644
--- a/README.md
+++ b/README.md
@@ -1,3 +1,3 @@
 # My notes
 
-My notes digitalized.
\ No newline at end of file
+This is the repository containing my digitalized notes for [wiki.bijl.us](https://wiki.bijl.us).
\ No newline at end of file
diff --git a/config/en/mkdocs.yaml b/config/en/mkdocs.yaml
index 1cf7201..7824462 100755
--- a/config/en/mkdocs.yaml
+++ b/config/en/mkdocs.yaml
@@ -66,6 +66,7 @@ nav:
     - 'Set theory':
       - 'Sets': mathematics/set-theory/sets.md
       - 'Relations': mathematics/set-theory/relations.md
+      - 'Maps': mathematics/set-theory/maps.md
     - 'Calculus': 
       - 'Limits': mathematics/calculus/limits.md
       - 'Continuity': mathematics/calculus/continuity.md
diff --git a/docs/en/index.md b/docs/en/index.md
index dd6974f..0812555 100644
--- a/docs/en/index.md
+++ b/docs/en/index.md
@@ -1 +1,3 @@
-# Welcome
\ No newline at end of file
+# Welcome
+
+Welcome to this web page where I have digitalized my notes from several fields.
\ No newline at end of file
diff --git a/docs/en/mathematics/set-theory/maps.md b/docs/en/mathematics/set-theory/maps.md
new file mode 100644
index 0000000..bd49eca
--- /dev/null
+++ b/docs/en/mathematics/set-theory/maps.md
@@ -0,0 +1,48 @@
+# Maps
+
+## Definition
+
+> *Definition*: a relation $f$ from a set $A$ to a set $B$ is called a map or function from $A$ to $B$ if for each $a \in A$ there is one and only one $b \in B$ with $afb$. 
+>
+> * To indicate that $f$ is a map from $A$ to $B$ we may write $f:A \to B$.
+> * If $a \in A$ and $b \in B$ is the unique element with $afb$ then we may write $b=f(a)$. 
+> * The set of all maps from $A$ to $B$ is denoted by $B^A$.
+> * A partial map $f$ from a $A$ to $B$ with the property that for each $a \in A$ there is at most one $b \in B$ with $afb$. 
+
+For example, let $f: \mathbb{R} \to \mathbb{R}$ with $f(x) = \sqrt{x}$ for all $x \in \mathbb{R}$ is a partial map, since not all of $\mathbb{R}$ is mapped.
+
+<br>
+
+> *Proposition*: let $f: A \to B$ and $g: B \to C$ be maps, then the composition $g$ after $f$: $g \circ f = f;g$ is a map from $A$ to $C$. 
+> 
+> ??? note "*Proof*:"
+> 
+>   Let $a \in A$ then $g(f(a))$ is an element in $C$ in relation $f;g$ with $a$. If $c \in C$ is an element in $C$ that is in relation $f;g$ with $a$, then there is a $b \in B$ with $afb$ and $bgc$. But then, as $f$ is a map, $b=f(a)$ and as $g$ is a map $c=g(b)$. Hence $c=g(b)=g(f(a))$ is the unique element in $C$ which is in relation $g \circ f$ with $a$. 
+
+<br>
+
+> *Definition*: Let $f: A \to B$ be a map.
+> 
+> * The set $A$ is called the *domain* of $f$ and the set $B$ the *codomain*. 
+> * If $a \in A$ then the element $b=f(a)$ is called the image of $a$ under $f$. 
+> * The subset of $B$ consisting of the images of the elements of $A$ under $f$ is called the image or range of $f$ and is denoted by $\text{Im}(f)$. 
+> * If $a \in A$ amd $b=f(a)$ then the element $a$ is called a pre-image of $b$. The set of all pre-images of $b$ is denoted by $f^{-1}(b)$. 
+
+Notice that $b$ can have more than one pre-image. Indeed if $f: \mathbb{R} \to \mathbb{R}$ is given by $f(x) = x^2$ for all $x \in \mathbb{R}$, then both $-2$ and $2$ are pre-images of $4$.
+
+If $A'$ is a subset of $A$ then the image of $A'$ under $f$ is the set $f(A') = \{f(a) \;|\; a \in A'\}$, so $\text{Im}(f) = f(A)$. 
+
+If $B'$ is a subet of $B$ then the pre-image of $B'$, denoted by $f^{-1}(B') is the set of elements $a$ from $A$ that are mapped to an element $b$ of $B'$.
+
+<br>
+
+> *Theorem*: let $f: A \to B$ be a map.
+>
+> * If $A' \subseteq A$, then $f^{-1}(f(A')) \supseteq A'$.
+> * If $B' \subseteq B$, then $f(f^{-1}(B')) \subseteq B'$.
+>
+> ??? note "*Proof*:"
+>
+>   Let $a' \in A'$, then $f(a') \in f(A')$ and hence $a' \in f^{-1}(f(A'))$. Thus $A' \subseteq f^{-1}(f(A'))$.
+>
+>   Let $a \in f^{-1}(B')$, then $f(a) \in B'$. Thus $f(f^{-1}(B')) \subseteq B'$.
\ No newline at end of file
diff --git a/docs/en/programming/start.md b/docs/en/programming/start.md
index e69de29..6b95b4f 100755
--- a/docs/en/programming/start.md
+++ b/docs/en/programming/start.md
@@ -0,0 +1,3 @@
+# Programming
+
+Welcome to the programming page.
\ No newline at end of file