This course is an introduction to classical Iwasawa theory, up to the proof of the Iwasawa main conjecture following Mazur and Wiles. We will begin with a review of results from algebraic number theory, class field theory etc. This will be followed by a study of $\mathbb{Z}_p$ extensions of number fields. We will then concentrate on the cyclotomic $\mathbb{Z}_p$ extensions of number fields. This will be followed by formulation of the Iwasawa main conjecture. For this part we need knowledge of $p$-adic $L$-functions. If time permits we will see Wilesâ€™s proof of the Iwasawa main conjecture.