  These are lecture notes from a course offered at the Bangalore School on
Statistical Physics - X, during 17-28 June 2019, [
https://www.icts.res.in/program/bssp2019 ] at International centre of
theoretical physics (ICTS), Bangalore. These pedagogical lectures are at the
introductory level, intended mainly for master/Ph.D. students or researchers
from outside the field. In these lectures, we discuss about the limit laws for
the sample mean and the maximum of a set of independent and identically
distributed (i.i.d.) random variables as well as random walks / Brownian
motion. The density of near-extreme events is also discussed. Finally, we
discuss the statistics of records for an i.i.d. random sequence as well as
random walks in discrete and continuous time. Some exercises are provided for
the students to work out. The video recording of the lectures are available at
https://www.icts.res.in/program/bssp2019/talks
