What is the ruling on fasting three days of Shawwal's six due to travel and study, and what is the ruling on fasting make-up days during the summer holiday?

Fasting six days of Shawwal is recommended (mustahabb), and whoever fasts some of them, it is hoped that they will receive a reward commensurate with what they have fasted. The full virtue is missed by whoever does not fast all six days. And whoever misses any of the six days and makes them up after Shawwal, it is hoped that they will receive their reward. As for making up for Ramadan, it is obligatory (wajib) at one's leisure, provided it is not delayed without an excuse until the next Ramadan begins.