Extracted from the website of Buddhist Vajrayana Charity Funds Association and translated (三世佛與三世劫) into English:

Buddhas of the Three Lifetimes and
Kalpas of the Three Lifetimes

What is meant by Three Lifetimes?  Three Lifetimes are the past life, the present life and the future life.
Buddhas of The Three Lifetimes are Buddha of the Past, Buddha of the Present and Buddha of the Future.
Kalpas of the Three Lifetimes (remark: a Kalpa is the period of time between the creation and re-creation of a world or universe) are Kalpa of the past, Kalpa of the present and Kalpa of the future.

(1)	Buddhas of The Three Lifetimes
Buddhas of the Past
●	Buddha Dipankara (Glorious Kalpa)
●	Buddha Kassapa (Wise/ Bhadra Kalpa)
●	《Great Treatise on the Perfection of Wisdom》(Fasc.9) records, “At the time Buddha Dipankara was born on Earth, there was light all over and around him and hence he was named Crown Prince Dipankara (a Sanskrit name meaning Lamp Bearer) at birth. He was also known as Buddha Dipankara when he attained Buddhahood.” Since everything all over and around him had been as bright as lamps when Buddha Dipankara was born and adding to the fact that he offered lamps to Buddhas, he was thus called Buddha Dipankara.
●	【Sutra of the Wise and the Foolish】(Fasc.3) says, “There was a state named Jambudvipa. Her prince whose name was Ushnisha (a Sanskrit word which means a three-dimensional oval at the top of the head of the Buddha) left the home life to become a monk and learned Buddhism. Having attained Buddhahood, he was called ‘Ushnisha Tathagata’. A Buddhist monk then lit candles every day as offerings to Buddha Ushnisha. The Buddhist monk therefore received his Niyatha Vivarana (assurance of future Buddhahood) from Buddha Ushnisha. He was told that he would come to be a Buddha in the future who would be known as Ding Guang Tathagata (note: that is Buddha Dipankara).” This was the origin that Buddha Dipankara had ever received Buddha Ushnisha’s prophecy in the past.
In terms of seniority, Buddha Dipankara, who has once foretold that Buddha Sakyamuni would succeed to accomplish Buddhahood after 91 Kalpas (it is said that: a Kalpa equals to 4 billion 320 million/ 4 320 000 000 years), is the enlightenment teacher of Buddha Sakyamuni. Later on, Buddha Sakyamuni attains Buddhahood in the present Wise Kalpa. Buddhists regard Buddha Sakyamuni as the Buddha of the Present whereas Buddha Dipankara is thus respectfully addressed as the Buddha of the Past by the people!
Buddha of the Present
●	Buddha Sakyamuni
●	The link between Ancient Buddha Dipankara and Buddha Sakyamuni is recorded in Volume I of【Tai-tzu-sui-ying-pen-chi-ching】. At the time when Buddha Sakyamuni was still a boy known as Sumedha (in his former incarnation), he came across a maiden named Gopika one day, who was holding seven Utpala flowers (it is also called Cyan Lotus which is a kind of flower that rises from mud. It is a symbol of pure). Sumedha bought the seven flowers from her and offered them to Buddha Dipankara. Afterwards, the boy found that there was a pool of sewage on the way where Buddha Dipankara was going to pass. Worrying that the holy feet of the Buddha would be dirtied; the boy undid his clothing, untied his hair and laid them both as well as having his own body spread out on top of the puddle of mud so that Buddha Dipankara could cross the sewage without soiling His feet. At the moment, Buddha Dipankara gave a Bestowal of Assurance for the boy, Sumedha, “You’re guaranteed to attain Buddhahood in Wise Kalpa which is 91 Kalpas from now and you’ll be known as Sakyamuni Tathagata by the time.” Having gone through the 91 Kalpas, Sumedha was later enlightened and attained Buddhahood. He is currently the founder of Buddhism, Buddha Sakyamuni!
Buddha of the Future
●	Buddha Maitreya
	His full name is Ajita Maitreya. The Sanskrit word, ‘Maitreya’ is His family name which means compassion and hence He is called the Compassionate Clan (ci shi) or the Compassionate Honoured One (ci zyun). The Sanskrit word, ‘Ajita’ is His given name which means invincible (wu neng sheng).
●	《Text on Questions Raised by Maitreya Bodhisattva》of【The Sutra of Ratnakuta】records, “In former Kalpas, Maitreya started learning Buddhism at a time earlier than Sakya. However, as Sakya had forged ahead more vigorously, He managed to attain Buddhahood before Maitreya did.”
●	It is also written in《Great Treatise on the Perfection of Wisdom》, “Many kalpas ago, both Sakya and Maitreya Bodhisattvas practised cultivation under the teaching of Buddha Phussa together. Having eulogized the Buddhas with a gatha (a verse recited in rhythm with the breath as part of the mindfulness practice) for seven days and nights, the meritorious virtue achieved by Sakya Bodhisattva enabled Him to surpass Maitreya Bodhisattva and attained Buddhahood nine kalpas earlier.” It is knowable that Maitreya Bodhisattva will be a successor of Buddha Sakyamuni to become the next Buddha.
●	Maitreya Bodhisattva was a disciple of Buddha Sakyamuni during his being a Bodhisattva in the last stage and he received his Niyatha Vivarana (prediction of future Buddhahood) from Sakyamuni, the World Honoured One.
	As recorded in【The Sutra of Maitreya’s Ascension】, “The Buddha declared in front of the public that Maitreya would be the next person to attain Buddhahood in the future. The Buddha gave Niyatha Vivarana to Maitreya to become the next Buddha who will still be known as Maitreya.”
●	Sakyamuni, the World Honoured One assured the future accomplishment of Buddhahood for Maitreya Bodhisattva. The incident is recorded in a great many sutras and among them, the earliest account can be found in the【Madhyamagama】(Fasc.13), “The Buddha said to the Buddhist monks that the arrival of the next Buddha on Earth who is known as Maitreya Tathagata will be in a remote time in the future when human’s lifespan is as long as eighty thousand years old.” Furthermore, in the【Sutra of the Wise and the Foolish】(Fasc.12卷十二) records, “All the people in the gathering have witnessed the World Honoured One’s (the Buddha’s) prediction of Maitreya becoming a Buddha in the future.” (The so-called ‘future’ is actually 5 billion 670 million/ 5 670 000 000 years of Earth time later. By the time, Maitreya Bodhisattva will be born on Earth from the inner court of Tusita Heaven (a deva-world where all Bodhisattvas destined to reach full Enlightenment in their next life dwell for a time). Leaving the home life to become a monk as well as learning Buddhism, Maitreya Bodhisattva actualizes the Way while seated beneath a Naga-puspa (a Dragon Flower tree) and attains Buddhahood.)
It is predicated in Buddhism that there are a thousand Buddhas appeared in each of the past Kalpa, the present Kalpa and the future Kalpa.
●	In Wise Kalpa, Buddhas of the Past were Buddha Kassapa and other Buddhas; Buddha of the Present is Buddha Sakyamuni while Buddhas of the Future will be Buddha Maitreya and other Buddhas.
●	If Glorious Kalpa and Wise Kalpa are calculated together: Buddha Dipankara acted as Buddha of the Past (Glorious Kalpa), Buddha of the Present is Buddha Sakyamuni (Wise Kalpa) whereas Buddhas of the Future will be Buddha Maitreya (Wise Kalpa) and other Buddhas.
(2)	Three Kalpas
Glorious Kalpa (Kalpa of the past)
●	A thousand Buddhas appeared
●	Buddha Dipankara (the 1st Buddha/some said He is the 428th Buddha) while the last three Buddhas of Glorious Kalpa were Buddha Vipasyin (the 998th Buddha), Buddha Sikhin (the 999th Buddha) and Buddha Visvabhu (the 1000th Buddha).
Wise Kalpa (Kalpa of the present)
●	A thousand Buddhas appear
●	Buddha Krakucchanda (the 1st Buddha), Buddha Kanakamuni (the 2nd Buddha), Buddha Kassapa (the 3rd Buddha), Buddha Sakyamuni (the 4th Buddha) and Buddha Maitreya (the 5th Buddha)
Constellation Kalpa (Kalpa of the future)
●	A thousand Buddhas are going to appear
Reference materials:
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