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

- Index of ramification, residual degree, norm of ideals for relative extensions of algebraic number fields and their properties. Fundamental equality.
- Different, Discriminant and Dedekind's theorem on ramified prime ideals in extensions of algebraic number fields.
- Finiteness of class number and determination of class numbers in special cases.
- Dirichlet's Density theorem and simple applications.
- Dirichlet's class number formula and its explicit determination for cyclotomic and quadratic fields in terms of L-series.

- M. Ram Murty and J. Esmonde, Problems in Algebraic Number Theory Springer-Verlag (2004).
- Saban Alaca and Kenneth Williams, Introductory Algebraic Number Theory Cambridge University Press (2003).
- Wladyslaw Narkiewikz, Elementary and Analytic Theory of Algebraic Numbers Springer-Verlag (2004).
- Erich Hecke, Lectures on the Theory of Algebraic Numbers Springer-Verlag, (1981).
- Paulo Ribenboim, Algebraic Numbers John Wiley and Sons (1972).