How could The power of Gravity be used to speed up space travel?

as in going from earth to Mars, etc. What about going from solar system to solar system? any hunches or ideas?
what speeds can the sling shot effect generate?

The power of gravity is already used (and has been used for decades - since earliest space travel). We physically can't build rockets big enough for direct trajectory launches of big space craft and probes (and certainly fort for manned craft). What we do is a low power take off to put the craft in orbit, then use slingshots. The most common in Earth, Venus, Venus, Earth to get out to the Giant planets then use the Giant planets to slingshot into the outer solar system (as Horizon will use to get out to Pluto).

The early Voyager and Pioneer probes did the same thing. This is why there are set launch windows (not weather based) If the sling shotting planet is not in the right position then the launch has to be delayed until it is.

We also use this same gravitational energy to slow craft down into orbit (no use picking up that much speed if you can't slow down again - and they don't carry anywhere near enough fuel/power to do that by engines - the engines are for manouvering only)

David H is correct. Slingshotting consists of the spacecraft approaching a planet from behind, and the planet's gravitational pull swings it around the planet and the spacecraft speeds up. It has extracted kinetic energy from the planet, which slows down in its orbit by a tiny amount.

the early astronomers after Copernicus couldn't explain the speeding up of planets. It is this slingshot thing these guys are talking about. comets do it too.