Algebraic number theory originated in attempts to solve Diophantine equations, the most notable of which is Fermat's last theorem, a conjecture that remained open for more than 300 years. The theory is now mature. Through factorizing ideals into products of prime ideals in number fields, one obtains numerous applications to problems in number theory and other fields of mathematics and science. The aim of this course is to introduce the student to this theory and endow him/her with the techniques necessary to perform computations and carry out proofs in this area.