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

Universal First-passage Properties of Discrete-time Random Walks and Levy Flights on a Line: Statistics of the Global Maximum and Records