A cycle is a circuit in which no vertex except the first (which is also the last) appears more than once.
Alternatively, a cycle can be defined as a closed path.
An $n$-cycle is a cycle with $n$ vertices.
The set of vertices and edges which go to make up a cycle form a subgraph.
This subgraph itself is also referred to as a cycle.
An odd cycle is a cycle with odd length, that is, with an odd number of edges.
An even cycle is a cycle with even length, that is, with an even number of edges.