Algebraic Number Theory: Algebraic numbers and algebraic integers, Class groups, Groups of units, Quadratic fields, Quadratic reciprocity law, Class number formula.
Analytic Number Theory: Fundamental theorem of arithmetic, Arithmetical functions, Some elementary theorems on the distribution of prime numbers, Congruences, Finite Abelian groups and their characters, Dirichlet theorem on primes in arithmetic progression.
Suggested books and references:
Narasimham, R., Raghavan, S., Rangachari, S. S. and Sunder Lal., Algebraic Number Theory, Lecture Notes in Mathematics, TIFR, 1966.
Niven, I. and Zuckerman, H. S., An Introduction to the Theory of numbers, Wiley Eastern Limited, 1989.
Apostol, T. M., Introduction to Analytic Number Theory, Springer International Student Edition, 1989.
Ireland, K. and Rosen, M., Classical Introduction to Modern Number Theory, Springer-Verlag (GTM), 1990.