Let $T^n$ be the real $n$-torus group. In this talk I will introduce a new generalized definition of lens spaces and give some sufficient conditions for diffeomorphic classification of lens spaces. I will show that any 3-dimensional lens space $L(p; q)$ is $T^2$-equivariantly cobordant to zero. This is the introductory part of a joint work with D. Y. Suh.