con ‧ do ‧ lence /kənˈdəʊləns $ -ˈdoʊ-/ BrE AmE noun [countable usually plural, uncountable]
[ Date: 1600-1700 ; Language: Late Latin ; Origin: condolere 'to express sympathy' , from Latin com- ( ⇨ COM- ) + dolere 'to feel pain' ]
sympathy for someone who has had something bad happen to them, especially when someone has died:
a letter of condolence
send/offer your condolences (=formally express your sympathy when someone has died)