diff --git a/main.pdf b/main.pdf
index 4250932..bd11d3a 100644
Binary files a/main.pdf and b/main.pdf differ
diff --git a/main.tex b/main.tex
index b9561de..8c00099 100644
--- a/main.tex
+++ b/main.tex
@@ -20,7 +20,8 @@
 \usepackage{graphicx}
 \usepackage{tikz}
 \graphicspath{{./images/}}
-
+% dependency graph
+\usetikzlibrary{positioning,arrows.meta}
 
 % --- Bibliography: biblatex + biber ---
 \usepackage[
@@ -71,6 +72,7 @@
 \mainmatter
 
 % Each chapter is in its own file and included as a subfile.
+\subfile{preface}
 \subfile{chapters/chap1}
 \subfile{chapters/chap2}
 \subfile{chapters/chap3}
diff --git a/preface.pdf b/preface.pdf
new file mode 100644
index 0000000..cf6bb83
Binary files /dev/null and b/preface.pdf differ
diff --git a/preface.tex b/preface.tex
new file mode 100644
index 0000000..db9bdf5
--- /dev/null
+++ b/preface.tex
@@ -0,0 +1,61 @@
+% preface.tex
+\documentclass[main.tex]{subfiles}
+
+\begin{document}
+
+\chapter*{Preface}
+\addcontentsline{toc}{chapter}{Preface}
+
+\section*{Philosophy}
+This book is intentionally small and opinionated:
+\begin{itemize}
+  \item Each chapter is a self-contained unit you can compile on its own.
+  \item Definitions are prioritized over intuition when the two conflict.
+  \item Every theorem should have an explicit list of dependencies:
+    what results it uses, and what background it assumes.
+\end{itemize}
+
+\section*{How to use the dependency graph}
+Think of the graph below as a diagnostic tool.
+If something feels like a black box, locate the nearest node you don’t fully own yet,
+then check the suggested “symptoms” under that node.
+
+\bigskip
+
+% --- Dependency tree graph (TikZ) ---
+\begin{figure}[ht]
+\centering
+\begin{tikzpicture}[
+  node distance=10mm and 18mm,
+  box/.style={draw, rounded corners, align=center, inner sep=4pt},
+  arrow/.style={-Latex}
+]
+
+\node[box] (lin) {Linear Algebra\\(bases, maps, eigenvalues)};
+\node[box, right=of lin] (real) {Real Analysis\\(limits, continuity, measure-lite)};
+\node[box, below=of lin] (prob) {Probability\\(expectation, variance, concentration)};
+\node[box, below=of real] (top) {Topology/Geometry\\(metrics, compactness)};
+
+\node[box, below=12mm of prob] (func) {Functional Analysis\\($L^p$, Hilbert spaces, operators)};
+\node[box, below=12mm of top] (quant) {Quantum Formalism\\(states, observables, partial trace)};
+
+\node[box, below=14mm of func, xshift=25mm] (book) {This Book\\(Chapters 1--n)};
+
+\draw[arrow] (lin) -- (func);
+\draw[arrow] (real) -- (func);
+\draw[arrow] (prob) -- (func);
+\draw[arrow] (func) -- (quant);
+\draw[arrow] (lin) -- (quant);
+\draw[arrow] (top) -- (quant);
+
+\draw[arrow] (func) -- (book);
+\draw[arrow] (quant) -- (book);
+\draw[arrow] (prob) -- (book);
+
+\end{tikzpicture}
+\caption{Dependency tree: prerequisites and how they feed into the main text.}
+\label{fig:dependency-tree}
+\end{figure}
+
+
+\end{document}