An adverb meaning 'finally' or 'at last,' used when something long-awaited or expected has happened.
彼は長年の研究の末、ついに新しい治療法を発表した。
After years of research, he finally announced a new treatment.
努力のかいあって、ついに試験に合格した。
Thanks to my efforts, I finally passed the exam.
台風が過ぎて、ついに青空が戻った。
The typhoon passed and finally the blue sky returned.
An adverb used with negative verbs to mean 'in the end' or 'after all (didn't happen),' indicating something expected did not occur.
何度も試したが、ついに解決できなかった。
I tried many times, but in the end I couldn't solve it.
約束していたのに、彼はついに現れなかった。
Even though he promised, he never showed up in the end.