• Linear Algebraic Aspects.- A brief introduction to index functions.- Relative Morse index .- The P-index theory.- The L-index theory.- Maslov type index for Lagrangian paths.- Revisit of Maslov type index for Symplectic Paths.- Applications of P-index.- Applications of L-index.- Multiplicity of brake orbits on a fixed energy surface.- The existence and multiplicity of solutions of wave equations.

“This book provides a very lucid and versatile introduction to the methods of index theories and their applications. It covers very important material in a concise and very instructive manner, and as such, it may serve as an excellent guide to further, more advanced and detailed reading in this area of mathematics.” (Ahmed Lesfari, zbMATH 1420.37001, 2019)