You can refer below books-

AERODYNAMICS

Fundamentals of Aerodynamics - John D. Anderson, Jr. Aerodynamics for Engineering Students - E.L. Houghton, P.W. Carpenter

OTHER REFERENCE BOOKS: Gas Dynamics - E. Rathakrishnan Modern Compressible flow - John D. Anderson, Jr.

FLIGHT MECHANICS (Performance, Stability & Control) Introduction to Flight - John

Here are the syllabus for GATE in Aero space engineering:

GATE Syllabus for Aerospace Engineering 2018

Section 1- Engineering Mathematics

Core Topics

• Linear Algebra

• Calculus

• Differential Equations

Special Topics

• Fourier Series

• Laplace Transform

• Numerical methods for linear and nonlinear algebraic equations

• Numerical integration and differentiation

Section 2- Flight Mechanics

Core

Yes, you can do the same and if you want to go for M.Tech through Gate so you can write the Gate exam in any specific branch but the eligibility criteria and the list of courses offered vary college to college. Some of the IITs which offer M.Tech in Aerospace

If you want low fees structure then you can take admission in the uiniversities like ISSUE Supero, TU Delft, Politécnico di Milano, Universidad Carlos III Madrid, Cranfield University, Moscow Aviation Institute.

You can also consider your admisson in America as there will be lot of scope in aerospace engineering. Fee

The fees structure of IIST Thiruvendapuram is Rs. 48,500 total. For the further detail you can go through with given below link (Page 5)

IIST Fees structure

Here are some of the colleges name you can prefer for Aerospace Engineering.

Indian Institute of Technology, Bombay through JEE Advance

Indian Institute of Technology, Kharagpur- JEE Advance

Indian Institute of Technology, Kanpur - JEE Advance

Indian Institute of Technology, Madras- JEE Advance

MIT Manipal - MUOET

For further detail

You can take admission through GATE in Aerospace engineering and you can opt for specialization like 

Aerodynamics

Thermodynamics/Propulsion

Aero-structures

Control and simulation

All the Best!!