#1 Srimad Bhagavatam is the literary incarnation of Krishna
Krsne sva dhamopagate dharma jnanadibhih saha
Kalau nasta-drsam esa puranarko dhunoditah
(Srimad Bhagavatam 1.3.43)
Srimad Bhagavatam is as luminous as the sun. After Lord Krishna left for His abode, accompanied by dharma and knowledge, Bhagavata Purana emerged to save the people from the darkness of Kali-yuga.
Muni, mora bhakta, ara grantha bhagavate
Yara bheda ache tara nasa bhalamate
(Chaitanya Bhagavata, Madhya, 21.18)
Myself (Supreme Lord), My devotees, and the scripture Srimad Bhagavatam – one who sees any distinction between these three will find all his intelligence destroyed.
#2 Exalted sages sing Srimad Bhagavatam for the benefit of all living entities
Bhakti yogam adhoksaje
Chakre satvata samhitam
Yasyam vai sruyamanayam
Krsne parama puruse
Bhaktir utpadyate pumsah
Soka moha bhayapaha
(Srimad Bhagavatam 1.7.6-7)
The excessive material miseries of the living entity can be directly mitigated by the process of Bhakti Yoga (Science of rendering devotional service); But this is unknown to the general mass and hence the learned sage Vedavyasa has compiled Srimad Bhagavatam, which is related to the Supreme truth. Simply by hearing Bhagavata Purana, the feeling for rendering devotional service to Krishna at once arises that extinguishes the fire of lamentation, illusion, and fearfulness within the heart.
#3 Srimad Bhagavatam is the Natural commentary on Brahma Sutra, Mahabharata, Gayatri and the Vedas
Artho yam brahma sutranam bharatartha vinirnayah
Gayatri bhasya rupo sau vedartha paribrmhitah
(Hari Bhakti vilasa 10.394)
Srimad Bhagavatam is the meaning of Brahma sutra. It is the conclusive meaning of Mahabharata. It reveals the inner meaning of the gayatri mantra and the essence of the Vedas.
Ataeva bhagavata karaha vichara
Iha haite pabe sutra srutira artha sara
(Chaitanya Charitamrita, madhya, 25.153)
(Chaitanya Mahaprabhu advised Prakashananda Sarasvati) Therefore, study Srimad Bhagavatam meticulously. Then you will understand the actual meaning and the essence of the Brahma Sutra.
#4 Srimad Bhagavatam is the essence of all scriptures
Saram saram samuddhrtam
(Srimad Bhagavatam, 1.3.41)
The essence of all Vedic literature and all histories has been amassed in Srimad Bhagavatam.
Sarva vedanta saram hi sri bhagavatam isyate
Tad rasamrta trptasya nanyatra syad ratih kvacit
(Srimad Bhagavatam 12.13.15)
Srimad Bhagavatam is indeed the essence of all Vedic literature and Vedanta philosophy. Whoever has tasted the transcendental mellow of Srimad Bhagavatam is never attracted to any other literature.
Krsna bhakti rasa svarupa sri bhagavata
Tate veda sastra haite parama mahattva
(Chaitanya Charitamrita, Madhya, 25.150)
Srimad Bhagavatam provides direct information about the mellows derived from serving Lord Krishna. Therefore Srimad Bhagavatam is higher than all other Vedic literatures.
Nigama kalpa taror galitam phalam
Suka mukhad amrta drava samyutam
Pibata bhagavatam rasam alayam
Muhur aho rasika bhuvi bhavukah
(Srimad Bhagavatam 1.1.3)
O expert and thoughtful men, relish Srimad Bhagavatam which is the essence of all Vedic literatures. It is the ripened fruit of the desire tree of Vedic knowledge. It has been sweetened by emanating from the mouth of Sukadeva Goswami. Therefore it has become even sweeter, although its nectarean juice was always relishable for all, including liberated souls.
#5 Inconceivable nature of Bhagavatam
Bhagavata, tulasi gangaya, bhaktajane
Caturdha vigraha krsna ei chari sane
(Chaitanya Bhagavata, Madhya, 22.81)
Wherever Srimad Bhagavatam, Tulasi devi and Ganges, and the devotees are found, Krishna is always present.
Mahacintya bhagavata sarvasastre gaya
Iha na bujhiye vidya tapa pratisthaya
Bhagavata bujhi heno yara ache jnana
Se na jane kabhu bhagavatera pramana
(Chaitanya Bhagavata, Madhya, 21.23-24)
According to all revealed scriptures, Srimad Bhagavatam is inconceivable, beyond mundane understanding. It cannot be understood either by scholarship, penance, or fame. One who is not a devotee of Krishna, no matter how great a scholar he may be, will never understand Srimad Bhagavatam.
Krsna tulya bhagavata vibhu, sarvasraya
Prati sloke prati aksare nana artha kaya
(Chaitanya Charitamrita, Madhya, 24.318)
Srimad Bhagavatam is as great as Krishna Himself, who is the Supreme Lord and the shelter of everything. Every verse and syllable of Srimad Bhagavatam, holds various meanings, for it is as limitless as Krishna.
#6 Studying and understanding Bhagavata Purana (Srimad Bhagavatam)
Avaisnava mukhodgirnam putam harikathamrtam
Sravanam naive kartavyam sarpocchistam yatha payah
Just as milk touched by the lips of a serpent is poison, similarly, Hari katha, when attended from the lips of non-devotees, is toxic. Those who speak and those who hear it will both suffer from the effects of the poison.
Vaishnava pasa bhagavata kara adhyayana
(Chaitanya Charitamrita, Antya, 13.113)
(Lord Chaitanya said to Raghunatha Bhatta) Study Srimad Bhagavatam under the tutelage of a pure Vaishnava who has realized God.
Yatha bhagavata pada vaisnavera sthane
Ekanta asraya kara chaitanya charane
(Chaitanya Charitamrita, Antya, 5.131)
If you want to understand Srimad Bhagavatam you must approach a self-realized Vaishnava and study under his tutelage while simultaneously taking the exclusive shelter of the lotus feet of Lord Chaitanya.