Cover, copyright page etc. are probably done outside Latex and later just combined as pdf.
Starting with the table of content the rest appears to be close to standard. i.e. using \documentclass{book} or \documentclass{scrbook} (Koma-scripts) will bring you very close to it.
Having an underlining rule in the header can certainly be done with these two classes. If you need more, have a look here: https://ctan.org/search?phrase=book .
Fonts used in those two books you can look up via the pdf's document properties. However, Latex has some built-in rules when to use which one.
Code follows in a minute, or two ;-) // Here it is:
\documentclass{book}
\newtheorem{Defi}{Definition} % for ch. 2
\begin{document}
\tableofcontents
\chapter{Review of classical mechanics}
In this lecture \ldots we will use in study of quantum mechanics.
\section{Newton's equation}
Let us consider a particle \ldots
[
V(x) = - \int_0^x dx' F(x')
]
This is a second order \ldots
\section{Lagrangian approach}
Another way to look at it \ldots
[
L = T - V \equiv L(x,\dot x)
]
% --- next one -----------------------
\chapter{Review of essential mathematics}
In the following few lectures \ldots
\section{Linear vector spaces}
\begin{Defi}
A set of quatities {$V_i$}, with a \ldots
\end{Defi}
We are using \ldots
\end{document}
Result as pdf-screenshots:



For a start it may be good to stay with the Latex defaults, which will take some time to conquer. Perhaps it's a good idea to start with an introductory book, which is simple enough. "The Latex companion" may be a good add-on; I think the second edition is also the last, from 2007. Since then there have been lots of extensions and improvements coming in various packages via CTAN.
Success :)
P.S.: See also here: https://ctan.org/topic/book-pub