The course starts with a review of various concepts of stochastic convergence (e.g. convergence in probability or in distribution) and properties of the multivariate normal distribution. Then the asymptotic properties of different statistical procedures are studied, including χ²-tests, Moment estimators, and M-estimators (including maximum likelihood estimations). The examples are chosen according to importance in practical applications, and the theory is motivated by practical relevance, but the subjects are presented in theorem-proof form.