श्रीबहुलाश्व उवाच -
कतिधा श्रीहरेर्विष्णोरवतारो भवत्यलम् ।
साधूनां रक्षणार्थं हि कृपया वद मां प्रभो ॥ १५ ॥
Bahulāśva says - To protect the pious ones how many avatars did Sri Vishnu take, please kindly tell me o Lord.
श्रीनारद उवाच -
अंशांशोंऽशस्तथावेशः कलापूर्णः प्रकथ्यते ।
व्यासाद्यैश्च स्मृतः षष्ठः परिपूर्णतमः स्वयम् ॥ १६ ॥
Narada said - O King. The avataras of Bhagavān are six types as told by sages like Vyāsa which are - amśa, amśāmśa, āveśa, kalā, pūrṇa and paripūrṇatama (or paripūrṇa).
अंशांशस्तु मरीच्यादिरंशा ब्रह्मादयस्तथा ।
कलाः कपिलकूर्माद्या आवेशा भार्गवादयः ॥ १७ ॥
Sages like Marīci are amśāmśa avatars, Brahma and his likes are amśā avatars. Paraśurāma and like are āveśa avatars.Kapila, Kūrma and the likes are kalā avatars.
पूर्णो नृसिंहो रामश्च श्वेतद्वीपाधिपो हरिः ।
वैकुण्ठोऽपि तथा यज्ञो नरनारायणः स्मृतः ॥ १८ ॥
Pūrṇa avatars are Narasimha, Śrī Rāma, śvetadvīpādhipati Hari, Vaikuntha, Yajna and Nara Nārāyaṇa.
परिपूर्णतमः साक्षाच्छ्रीकृष्णो भगवान् स्वयम् ।
असंख्यब्रह्माण्डपतिर्गोलोके धाम्नि राजते ॥ १९ ॥
Śrī Krishna is Paripūrṇatama avatar who is the lord of infinite Brahmāṇḍas and who resides in Goloka.
कार्याधिकारं कुर्वन्तः सदंशास्ते प्रकिर्तिताः ।
तत्कार्यभारं कुर्वन्तस्तेंऽशांशा विदिताः प्रभोः ॥ २० ॥
Those who like Brahma take up the authority of works like creation etc., are the sāttvic amśa avatars of Lord. Those who help in such works are amśāmśa avatars like Marīci and other prajāpatis.
येषामन्तर्गतो विष्णुः कार्यं कृत्वा विनिर्गतः ।
नानाऽऽवेषावतारांश्च विद्धि राजन्महामते ॥ २१ ॥
The all pervading vishnu who resides in the inner heart with his power to accomplish a certain work and leaves the person or body (though the person doesn't die) after the accomplishment, such avatars like Paraśurāma are called āveśa avatars.
धर्मं विज्ञाय कृत्वा यः पुनरन्तरधीयत ।
युगे युगे वर्तमानः सोऽवतारः कला हरेः ॥ २२ ॥
In every Yuga, when the Lord descends to earth, protects and establishes the dharma and takes back his avatara after that is called kalā avatar.
चतुर्व्यूहो भवेद्यत्र दृश्यन्ते च रसा नव ।
अतः परं च वीर्याणि स तु पूर्णः प्रकथ्यते ॥ २३ ॥
Where the four vyūhas are manifested like Rāma, Lakshmana, Bharata and Satrughna are manifestations of Vasudeva, Sankarshana, Pradyumna and Anirudhas (four vyūhas of Vishnu), where nine rasās are visible and where the utmost valour, power and strength are manifested like Rāma, Narasimha such avatars are called Pūrṇa avatars.
यस्मिन्सर्वाणि तेजांसि विलीयन्ते स्वतेजसि ।
तं वदन्ति परे साक्षात्परिपूर्णतमं स्वयम् ॥ २४ ॥
Paripūrṇatama avatar is the one in whos tejas, the tejas (lusture and splendour in all their fullness) of all other avatars gets absorbed.
Garga Samhita is a great book also called Garga Bhagavatam. The Hindi prose version is available here.
