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Abstract: A fundamental aspect of a random walk is determining when it reaches a specified threshold position for the first time. This first-passage time, and more generally, the distribution of first passage times underlies many non-equilibrium phenomena, such as the triggering of integrate and fire neurons, the statistics of cell division, and the execution of stock options. The computation of the first-passage time and its distribution is both simple and beautiful, with profound connections to electrostatic potential theory. I will present some aspects of these fundamentals and then discuss applications of first-passage ideas to diverse phenomena, including stochastic search processes and a toy model of wealth sharing.