sympathy:
1. feelings of pity and sorrow for someone else's misfortune;
'they had great sympathy for the flood victims'
2. understanding between people; common feeling.
'the special sympathy between the two boys was obvious to all'
empathy:
the ability to understand and share the feelings of another.
compassion:
sympathetic pity and concern for the sufferings or misfortunes of others.
'the victims should be treated with compassion'
(as given by google)