keen

1 keen /ˈkiːn/ adjective
keener; keenest
1 keen
/ˈkiːn/
adjective
keener; keenest
Britannica Dictionary definition of KEEN
[also more keen; most keen]
1 
: having or showing an ability to think clearly and to understand what is not obvious or simple about something
2 
: very strong and sensitive : highly developed
3 
a  : very excited about and interested in something
b  : feeling a strong and impatient desire to do something
4 
: strong or intense
5 
informal + old-fashioned : very good : wonderful
◊ This sense is now usually used in a playful or ironic way.
— see also peachy keen
6 
literary : having a sharp edge or point
7 
British, of a price : very low

(as) keen as mustard

British
: very excited and interested : very enthusiastic

keen on

1 
: very excited about and interested in (something)
2 
chiefly British : interested in or attracted to (someone)

— keenly

adverb

— keenness

/ˈkiːnnəs/ noun
2 keen /ˈkiːn/ verb
keens; keened; keening
2 keen
/ˈkiːn/
verb
keens; keened; keening
Britannica Dictionary definition of KEEN
[no object] old-fashioned + literary
: to make a loud and long cry of sorrow