In Vedic Astronomy (Drik Ganita), each lunar month is named after the Nakshatra in which the Full Moon (Purnima) occurs, and corresponds to the Sun's transit (Sankranti) into a specific zodiac sign.
Amanta System (South & West India) ends on Amavasya (New Moon). Purnimanta System (North & Central India) ends on Purnima (Full Moon).
Every ~32.5 lunar months, when a lunar month has no Solar Sankranti (Sun doesn't change zodiac sign), an intercalary Adhika Masa (Purushottama Masa) is added.

Month 1 of Vedic Lunar Year. Full moon occurs in Chitra Nakshatra. Starts with Nav Varsh (Gudi Padwa / Ugadi). Features Ram Navami, Chaitra Navratri & Hanuman Jayanti.
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Month 2. Full moon occurs in Vishakha Nakshatra. Sacred for Vishnu worship and water donation. Features Akshaya Tritiya, Narasimha Jayanti & Buddha Purnima.
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Month 3. Full moon occurs in Jyeshtha Nakshatra. Month of intense tapasya and water preservation. Features Ganga Dussehra, Nirjala Ekadashi & Vat Savitri Vrat.
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Month 4. Full moon occurs in Ashadha Nakshatra. Beginning of Dakshinayana & 4-month Chaturmas. Features Puri Jagannath Rath Yatra, Devshayani Ekadashi & Guru Purnima.
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Month 5. Full moon occurs in Shravana Nakshatra. Holiest month for Shiva devotion, Shravan Somvar Vrats, Kanwar Yatra, Nag Panchami & Raksha Bandhan.
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Month 6. Full moon occurs in Bhadrapada Nakshatra. Celebrates divine incarnations. Features Krishna Janmashtami, Hartalika Teej, Ganesh Chaturthi & Anant Chaturdashi.
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Month 7. Full moon occurs in Ashwini Nakshatra. Dedicated to Shakti worship. Features Pitru Paksha Tarpan, Sharad Navratri, Vijayadashami (Dussehra) & Sharad Purnima.
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Month 8. Full moon occurs in Krittika Nakshatra. Holiest month for Deep Daan. Features Karva Chauth, Dhanteras, Diwali Lakshmi Puja, Govardhan Puja, Chhath & Tulsi Vivah.
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Month 9. Full moon occurs in Mrigashira Nakshatra. Honored by Lord Krishna in Bhagavad Gita. Features Vivah Panchami, Gita Jayanti & Dattatreya Jayanti.
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Month 10. Full moon occurs in Pushya Nakshatra. Month of Surya Deva worship and charity. Features Makar Sankranti (Uttarayana), Pongal & Pausha Putra Ekadashi.
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Month 11. Full moon occurs in Magha Nakshatra. Holy month for Prayagraj Sangam baths and wisdom. Features Vasant Panchami (Saraswati Puja), Ratha Saptami & Bhishma Ashtami.
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Month 12 (Final month of Hindu Lunar Year). Full moon occurs in Phalguni Nakshatra. Features Maha Shivaratri, Holika Dahan & Rangwali Holi.
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