  We investigate the cosmological solutions of the $f(T)$ gravity theory using
the method of dynamical systems. For this purpose a general form of the $f(T)$
function is considered and four conditions are defined that they have to
satisfy in order to describe the standard cosmological history. We examine the
power law, and another form of $f(T)$ against these conditions. For a power law
function $f(T)= B(-T)^\beta$, $\beta$ must be less than one and unequal to
$\frac{1}{2}$ to obtain a consistent cosmological model. We also investigate a
model of inflation in this theory.
