The science of orbital mechanics grew out of the attempts at finding approximate solutions to the Newton’s three-body problem. Two solutions have been of partic-ular interest in the context of the interplanetary trajectory design: the Hohmann trajectories and the gravity-assist trajectories. The ideal Hohmann trajectories serve mostly as planning benchmarks; the proximate Hohmann trajectories are usually employed for flights to the targets close to Earth. Gravitational interaction between a planet and an approaching spacecraft may result in the spacecraft being catapulted into a higher orbit or being slowed down. Trajectories modified by such actions are referred to as the gravity-assist (or gravity-assisted) trajectories. Such trajectories make possible reaching the distant and/or difficult targets. The Hohmann trajectories and gravity-assist trajectories may be combined into composite trajectories. The NASA spacecraft Voyager-2 (launched in 1977) flew along a Hohmann ellipse to Jupiter, then it executed gravity-assist flybys of Jupiter (1979), Saturn (1981), Uranus (1986), and Neptune (1989). The encounter with Neptune catapulted Voyager-2 out of the Solar System. The gravity-assist flybys allow manipulation of the orbits of the captured probes. The NASA/ESA/ASI Cassini-Huygens mission provides an extreme example: each Titan flyby has been used to shape the probe’s orbits around Saturn. It is anticipated that before the end of the mission (2017), over a hundred Titan gravity-assist flybys will take place. In every system of two massive bodies there exist five points, the Lagrange or libration points, around which a constant-pattern revolution by a third body of negligible mass may be maintained with a small expenditure of fuel. These quasi-circular trajectories are known as the halo orbits. In the Sun-Earth system, the point L1 offers unobstructed observations of the Sun, while the point L2 offers a wide-sky visibility. The first spacecraft that orbited the point L1 was the NASA/ESA International Sun Explorer 3 (1978). The NASA probe Genesis visited both points, L1 and L2 (2004). The weak stability zones between the planetary bodies allow further development of the nonconventional trajectories. Gliding through the weak stability zone in the Moon-Earth system, the ESA probe SMART-1 reached the Moon after thirteen months (2004). Lagrangian trajectories connect weak stability zones of all the major bodies in the Solar System. These trajectories constitute a constantly changing grid referred to as the Planetary Transport Network. The NASA/JPL Deep Space Network (DSN) provides tracking and navigation for the flights within the Solar System.