  These lectures notes aim at introducing L\'{e}vy processes in an informal and
intuitive way, accessible to non-specialists in the field. In the first part,
we focus on the theory of L\'{e}vy processes. We analyze a `toy' example of a
L\'{e}vy process, viz. a L\'{e}vy jump-diffusion, which yet offers significant
insight into the distributional and path structure of a L\'{e}vy process. Then,
we present several important results about L\'{e}vy processes, such as infinite
divisibility and the L\'{e}vy-Khintchine formula, the L\'{e}vy-It\^{o}
decomposition, the It\^{o} formula for L\'{e}vy processes and Girsanov's
transformation. Some (sketches of) proofs are presented, still the majority of
proofs is omitted and the reader is referred to textbooks instead. In the
second part, we turn our attention to the applications of L\'{e}vy processes in
financial modeling and option pricing. We discuss how the price process of an
asset can be modeled using L\'{e}vy processes and give a brief account of
market incompleteness. Popular models in the literature are presented and
revisited from the point of view of L\'{e}vy processes, and we also discuss
three methods for pricing financial derivatives. Finally, some indicative
evidence from applications to market data is presented.
