Discrete kinetic shear Alfvén modes driven by ion temperature gradient (AITG) are investigated in the full gyrokinetic limit. It is shown that AITG instability may occur when the plasma pressure gradient is well below the threshold value for ideal MHD ballooning instabilities and that the critical magnetic shear required to completely stabilize the former is significantly higher than that for the latter. In addition, finite-β (=plasma pressure/magnetic pressure) effects on toroidal electrostatic ion temperature gradient (ITG) modes are studied, and the coexistence of AITG and ITG in a certain parameter regime is demonstrated. The effects of AITG instabilities on plasma confinement are discussed.