What is Tithi?
Tithi (తిథి / திதி) is the lunar day in the Hindu calendar. It is defined as the time taken for the longitudinal angle between the Moon and Sun to increase by 12°. There are 30 tithis in a lunar month — 15 in the waxing moon fortnight (Shukla Paksha) and 15 in the waning moon fortnight (Krishna Paksha).
The 30 Tithis
Shukla Paksha (Waxing Moon — 1 to 15): Pratipada, Dwitiya, Tritiya, Chaturthi, Panchami, Shashthi, Saptami, Ashtami, Navami, Dashami, Ekadashi, Dwadashi, Trayodashi, Chaturdashi, Purnima (Full Moon)
Krishna Paksha (Waning Moon — 1 to 15): Same names, ending with Amavasya (New Moon)
Auspicious and Inauspicious Tithis
Generally auspicious: Pratipada, Dwitiya, Tritiya, Panchami, Saptami, Dashami, Ekadashi, Dwadashi, Trayodashi, Purnima
Generally avoided for new work: Chaturthi, Ashtami, Chaturdashi, Amavasya (especially for new beginnings and marriages)