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The conventional method to design a spacecraft trajectory from Earth to Moon is by Hohmann transfer. This type of transfer uses only two-body dynamics. We will describe alternative paths to the Moon using three-body and four-body dynamics. These new types of trajectories are more fuel efficient but take a longer time. In particular, we will discuss ballistic lunar capture transfers, which have the unique property that upon arrival at the Moon, the spacecraft is automatically captured in an elliptical orbit about the Moon, without the use of rockets. Such transfers can be designed using the mathematical concept of Weak Stability Boundary, which will be illustrated in this lecture. This talk is based on joint work with Edward Belbruno (Princeton University) and Francesco Topputo (Polytechnic University of Milan).