Final answer:
Taylor Swift's album "1989" won a Grammy for Album of the Year and had three #1 hits: 'Shake It Off', 'Blank Space', and 'Bad Blood'.
Step-by-step explanation:
The album of Taylor Swift's that won a Grammy for Album of the Year and yielded three #1 hits is "1989". It marked a significant shift in her musical style from country to pop. The album includes hits such as 'Shake It Off', 'Blank Space', and 'Bad Blood', all of which reached #1 on the Billboard Hot 100 chart. Winning the Grammy for Album of the Year in 2016, "1989" solidified Swift's status as a pop powerhouse.