Tenant wants to leave early

Tenancy Types and Management

He has currently been in the flat for 2 months (at the end of October) and signed a 6 month AST with periodic tenancy following that.

I guess my questions are,

- can he leave, and if so how much does rent will he have to pay me, another 4 months worth?

- Are there any other expenses i can reclaim from him, such as the cost for finding new tenants?

- Is there anything else anyone can think of i should be aware of.

Many thanks for your time

Hugh