diff --git a/Chapters/15-Appendix-A/INDEX.md b/Chapters/15-Appendix-A/INDEX.md
index 1d68956..f32da2c 100644
--- a/Chapters/15-Appendix-A/INDEX.md
+++ b/Chapters/15-Appendix-A/INDEX.md
@@ -120,6 +120,66 @@ H(f) = \begin{bmatrix}
 \end{bmatrix}
 $$
 
+## [Flow](https://en.wikipedia.org/wiki/Flow_(mathematics))[^wiki-flow]
+
+A flow over a set $A$ is a mapping of $R$ over $A$:
+
+$$
+a \in A, t \in \R \\
+\varphi(a, t) \in A
+$$
+
+Moreover, since $\varphi(a, t) \in A$ it also applies:
+
+$$
+a \in A, t \in \R, s \in \R \\
+\begin{aligned}
+    \varphi(\varphi(a, t), s) &= \varphi(a, t + s) \in A \\
+    \varphi(a, 0) &= a
+\end{aligned}
+$$
+
+In other words, applying a flow over a flow of a variable is like applying
+the flow over the variable and the sum of real numbers (think of summing times).
+
+Also, 0 is the neutral element of a flow.
+
+## [Vector Field](https://en.wikipedia.org/wiki/Vector_field)[^wiki-vector-field]
+
+It is a mapping from from a set $A \subset \R^n$ so that:
+
+$$
+V: A \rightarrow \R^n
+$$
+
+So, this means that for each element of $A$, which we can consider point, it
+associates another vector, which we may consider a velocity (but also points).
+
+So, in a way, it can be seen as the amount of movement of that point in space.
+
+## Change of Variables in probability[^stack-change-var]
+
+let's change from 2 random variables, $X$ and $Y$ where $X$ has a CDF that is $F_X$
+and $Y = g(X)$ and $g$ is monotonic:
+
+$$
+\begin{aligned}
+    P(Y \leq y) &= P(g(X) \leq y) =  P(g^{-1}(g(X)) \leq g^{-1}(y)) = \\
+    &= P(X \leq x) \rightarrow \\
+    \rightarrow F_Y(y) &= F_X(x) = F_X(g^{-1}(y))
+\end{aligned}
+$$
+
+Now, let's derive both handles of the equation for y:
+
+$$
+f_Y(y) = f_X(g^{-1}(y)) \cdot \frac{d\, g^{-1}(y)}{d \, y}
+$$
+
+> [!NOTE]
+> In case x and y are in higher dimensions, the last term is the determinant of
+> the Jacobian matrix, or Jacobian
+
 [^khan-1]: [Khan Academy | Laplace Intuition | 9th November 2025](https://www.youtube.com/watch?v=EW08rD-GFh0)
 
 [^wiki-cross-entropy]: [Wikipedia | Cross Entropy | 17th November 2025](https://en.wikipedia.org/wiki/Cross-entropy)
@@ -127,3 +187,9 @@ $$
 [^wiki-entropy]: [Wikipedia | Entropy | 17th November 2025](https://en.wikipedia.org/wiki/Entropy_(information_theory))
 
 [^wiki-pca]: [Wikipedia | Principal Component Analysis | 18th November 2025](https://en.wikipedia.org/wiki/Principal_component_analysis#Computation_using_the_covariance_method)
+
+[^wiki-flow]: [Wikipedia | Flow (Mathematics) | 23rd November 2025](https://en.wikipedia.org/wiki/Flow_(mathematics))
+
+[^wiki-vector-field]: [Wikipedia | Vector Field |23rd november 2025](https://en.wikipedia.org/wiki/Vector_field)
+
+[^stack-change-var]: [StackExchange | Derivation of change of variables of a probability density function? | 25th November 2025](https://stats.stackexchange.com/questions/239588/derivation-of-change-of-variables-of-a-probability-density-function)
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