\chapter{Summary of part \ref{kerr}}
Let us recall that while there are certain similarities between geodesics in the equator of the Kerr black holes and spherically symmetric solutions (Schwarzschild and Reissner Nordstr\"om), (for example the function f$(u)$ is cubic, as it is in the case of the Schwarzschild black hole, so unlike in the Reissner-Nordstr\"om case, equatorial geodesics of the Kerr black hole can reach the singularity), rotation of the black hole adds a new feature, so now we have to distinguish between direct and retrograde orbits. Also the radial geodesics are ``dragged" around the black hole.

Besides the three conservation laws (the energy, the angular momentum and the norm of the four-velocity), in the Kerr space-time there is the fourth conserved quantity, the Carter constant, which discovery followed from demonstrating the separability of the Hamilton-Jacobi equation. That is why
it is possible to find  the  general solution of orbits outside the equatorial plane, (the function f$(r)$ is quartic), although the solution is not explicit.
 As before, in the case of geodesics of the Schwarzschild and Reissner-Nordstr\"om black holes, only time-like geodesics can be bound.

This thesis extends previous work of \cite{chandrasekhar} by giving general solutions of time-like, space-like and null orbits in equatorial plane in slow, extreme and fast black holes, and by studying special types of non-equatorial time-like, space-like and null geodesics in complete detail. General observation about relationship between parameters and types of orbits were made in addition to work of \cite{onil}. 