  We explore an extension of the symmetric teleparallel gravity denoted the
$f(Q)$ theory, by considering a function of the nonmetricity invariant $Q$ as
the gravitational Lagrangian. Some interesting properties could be found in the
$f(Q)$ theory by comparing with the $f(R)$ and $f(T)$ theories. The field
equations are derived in the $f(Q)$ theory. The cosmological application is
investigated. In this theory the accelerating expansion is an intrinsic
property of the universe geometry without need of either exotic dark energy or
extra fields. And the state equation of the geometrical dark energy can cross
over the phantom divide line in the $f(Q)$ theory. In addition, the dynamical
system method are investigated. It is shown that there are five critical points
in the STG model for taking $f(Q)=Q+\alpha Q^2$. The critical points $P_{4}$
and $P_{5}$ are stable. $P_{4}$ corresponds to the geometrical dark energy
dominated de Sitter universe ($w_{tot}^{eff}$=-1), while $P_{5}$ corresponds to
the matter dominated universe ($w_{tot}^{eff}$=0). Given that $P_{4}$
represents an attractor, the cosmological constant problems, such as the fine
tuning problem, could be solved in the STG model.
