**[Cr:4, Lc:3, Tt:1, Lb:0]**

- Characteristic and minimal polynomial of an element relative to a finite extension, Equivalent definitions of norm and trace, Algebraic numbers, algebraic integers and their properties.
- Integral bases, discriminant, Stickelberger's theorem, Brille's theorem, description of integral basis of quadratic, cyclotomic and special cubic fields.
- Ideals in the ring of algebraic integers and their norm, factorization of ideals into prime ideals, generalised Fermat's theorem and Euler's theorem.
- Dirichlet's theorem on units, regulator of an algebraic number fields, explicit computation of fundamental units in real quadratic fields.
- Dedekind's theorem for decomposion of rational primes in algebraic number fields and its application, splitting of rational primes in quadratic and cyclotomic fields.

- Saban Alaca and Kenneth Williams, Introductory Algebraic Number Theory, Cambridge University Press (2003).
- M. Ram Murty and J. Esmonde Problems in Algebraic Numbers Theory, Springer-Verlag (2004).
- Wladyslaw Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers, Springer-Verlag (2004).
- Erich Hecke, Lectures on the Theory of Algebraic Numbers, Springer-Verlag (1981).
- Paula Ribenboim, Algebraic Numbers, John Wiley & Sons (1972).
- Harry Pollard and Harold Diamond, The Theory of Algebraic Numbers, Dover Publications (2010).