Booklist

Books in queue: (* means the books is currently working on.)

Spectral and Algebraic Graph Theory by Daniel A. Spielman
Lecture notes on Differential Geometry by Eckhard Meinrenken
Discrete Differential Geometry: An Applied Introduction by Keenan Crane
Laplacian Eigenvectors of Graphs: Perron–Frobenius and Faber–Krahn Type Theorems by Türker Biyikoglu, Josef Leydold, Peter F. Stadler
Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs by Jason J. Molitierno
Some applications of the Laplace eigenvalues of graphs by Bojan Mohar
Eigenvalues in combinatorial optimization by Bojan Mohar and Svatopluk Poljak
Spectral graph theory by Fan Chung
Spectres de Graphes by Y. Colin de Verdière
Algebraic Graph Theory by Chris Godsil and Gordon F. Royle
Theory of Quantum Information by John Watrous
Topics in Algebraic Graph Theory by Lowell W. Beineke, Robin J. Wilson, and Peter J. Cameron.
Explorations in Algebraic Graph Theory with Sage by Chris Godsil and Robert A. Beezer.
Algorithms and Spectral Graph Theory by Joseph Cheriyan
Combinatorics: The Art of Counting by Bruce Sagan
Quantum Computation and Quantum Information by Michael Nielsen and Isaac Chuang

Algebraic Geometry: (suggestions from forum, Boris's paper)

Real Algebraic Geometry by Jacek Bochnak, Michel Coste, and Marie-Francoise Roy
Algorithms in Real Algebraic Geometry by Saugata Basu, Richard Pollack, and Marie-Francoise Ë Roy
keywords: Tarski–Seidenberg theorem

Inverse Eigenvalue Problem:

Eigenvalues, Multiplicities and Graphs by Charles R. Johnson and Carlos M. Saiago
Inverse Problems in Vibration by Graham Gladwell
Inverse Eigenvalue Problems: Theory, Algorithms, and Applications by Gene H. Golub and Moody Chu

Graph Drawing

http://graphdrawing.org/
Handbook of Graph Drawing and Visualization by Roberto Tamassia (Editor)
Graph Drawing: Algorithms for the Visualization of Graphs by Giuseppe Di Battista, Peter Eades, Roberto Tamassia, and Ioannis G. Tollis

Books finished: