  In these lecture notes I will discuss the universal first-passage properties
of a simple correlated discrete-time sequence {x_0=0, x_1,x_2.... x_n} up to n
steps where x_i represents the position at step i of a random walker hopping on
a continuous line by drawing independently, at each time step, a random jump
length from an arbitrary symmetric and continuous distribution (it includes,
e.g., the Levy flights). I will focus on the statistics of two extreme
observables associated with the sequence: (i) its global maximum and the time
step at which the maximum occurs and (ii) the number of records in the sequence
and their ages. I will demonstrate how the universal statistics of these
observables emerge as a consequence of Pollaczek-Spitzer formula and the
associated Sparre Andersen theorem.
