Lectures on Convex Optimization is devoted to well structured
and efficiently solvable convex optimization problems, with
an emphasis on conic quadratic and semidefinite programming.
The authors begin with linear programming, and then progress
to conic programming. [I really enjoyed their description
of the transition from linear to general conic
programming!]. They then discuss two special conic
optimization problems namely second order cone programming,
and semidefinite programming. Numerous applications of conic
programming espcially in filter design, Lyapunov stability
analysis, and structural design are presented. The book concludes with
a discussion on the computational tractability of convex
programs, and primal dual interior point algorithms to
solving general conic optimization problems.

One can then take on the likes of Renegar's recent book
on interior point methods, and
Nesterov and Nemirovski's seminal treatise on the general
theory of interior point methods in convex optimization,
at a more advanced level.

My only minor comments are :-
(a) The organization of the book as a series of 6 lectures
is misleading, since there is quite a lot of material
covered in each lecture.
(b) The book has a very short [almost
nonexistent] bibliography.

All in all, a good workout and an encyclopedic source for
anyone interested in theory and applications of convex
optimization. Highly recommended!.