homesickness(missing one's home or family) noun [UK: ˈhəʊm.sɪk.nəs] [US: ˈhoʊm.sɪk.nəs]
longing [longings](melancholic desire) noun [UK: ˈlɒŋ.ɪŋ] [US: ˈlɔːŋ.ɪŋ]He is longing for city life. = Ha nostalgia della vita di città.
nostalgia(bittersweet yearning for the things of the past) noun [UK: nɒ.ˈstæl.dʒə] [US: nɒ.ˈstæl.dʒə]The joy we shared together still fills my heart with warmth and nostalgia. = La gioia che abbiamo condiviso insieme mi riempie ancora il cuore di calore e nostalgia.
yearning [yearnings](wistful or melancholy longing) noun [UK: ˈjɜːn.ɪŋ] [US: ˈjɝːn.ɪŋ]