First layer, an explanation of the title (The full title of Amitabha Sutra is called The Amitabha Sutra Spoken by the Buddha).
This Sutra takes its name from the one who expounds it and the one who is the subject of the exposition. "The Buddha" refers to the Teacher who expounds the doctrine in this world — namely, Sakyamuni Buddha. Driven by the power of His vows of great compassion, He was born into this World of Five Turbidities. He is the One who, having awakened first, awakens those who come after; He is the One who knows it all and sees it all. He speaks the Sutra with joy in His heart. A Buddha's intent is to liberate sentient beings. Since the conditions for beings to attain enlightenment have ripened, the Buddha expounds these Pure Land teachings which are difficult to believe, enabling all beings to reach ultimate liberation. That's why He rejoices.
"Amitabha" refers to the One of whom Sakyamuni speaks in the Sutra, which is the subject of the exposition, the Teacher of the Pure Land. Through His Forty-eight Great Vows, He receives sentient beings who possess faith, aspiration, and mindfulness of the Buddha, guiding them to birth in the Pure Land of Ultimate Bliss and ensuring they attain the stage of non-retrogression forever. The Sanskrit term of Amitabha means both "Infinite Life" and "Infinite Light." The essential point is that everything about Amitabha Buddha is infinite: His merits and wisdom, His supernatural powers and efficacy, His land and embodiment, His teachings and deliverance of sentient beings.
"Sutra" is the general designation for all teachings delivered by the Buddha's golden mouth.
The above-mentioned terms taken together make up the title of the scripture: The Amitabha Sutra Spoken by the Buddha. The three aspects - teaching, practice, and principle - are each explained in both general and particular senses, as detailed in the Tiantai system, explicitly and extensively.
