There are several ligaments around the knee which may become injured. Not all require Surgery, some get better with non-operative intervention. Some often need surgery.
Anterior cruciate ligament (ACL), Posterior cruciate ligament (PCL), Medial collateral ligament (MCL), Lateral collateral ligament (LCL) and the Posterolateral corner (PLC), form the key ligaments around the knee.
Some of these ligaments are injured in isolation some may get injured with other ligaments.
See presentation on Knee Ligament Injuries.
Ask your doctor / specialist for more information