forge ahead with one's work
仕事を着実にこなす
forge closer [stronger] links with industry
産業界ともっと密[強固]な関係を築く
Forget about him.
もう彼のことは忘れなさい
forget one's worries at the piano
ピアノを弾いて悩みを忘れる
forget the whole thing
御破算にする
Forget your worries and drink up.
心配ごとを忘れて一杯あけてくれ
forgive (him) his debt
彼の借金を棒引きする
forgive a sin [an insult]
罪[無礼]を許す[許してやる]
Forgive me for keeping you waiting.
お待たせしてすみません(◆Forgive my keeping you waiting. ともいえる)
Fork it over to me.
それをよこせ