Gyan
Panchang, nakshatras, the darshanas, karma and dharma, explained simply.
The 27 Nakshatras
The Moon's twenty-seven houses, their deities and their symbols
Nakshatras are the 27 'lunar mansions' of Indian astronomy: equal segments of 13°20′ along the Moon's path, each named after a star or star group. The Moon passes through roughly one nakshatra a day. Each has a presiding Vedic deity and a traditional symbol, and nakshatras are used in the panchang to time festivals, rites and naming ceremonies.
Dharma, Karma and Moksha
Right living, the law of action and liberation, with the four goals and four stages of life
Dharma is the right way of living that sustains oneself and the world; karma is action and the law that every action bears fruit; moksha is liberation from the cycle of rebirth. Hindu tradition places them within the four goals of life (purusharthas: dharma, artha, kama, moksha) and the four stages of life (ashramas: student, householder, retiree, renunciate).
The Four Yugas and the Cosmic Cycle
Satya, Treta, Dvapara and Kali: the ages of the world as the texts count them
Hindu texts describe time as cyclical. A great cycle (chaturyuga) is made of four ages, Satya (Krita), Treta, Dvapara and Kali, in a ratio of 4:3:2:1, with dharma declining by a quarter in each. The Manusmriti gives the cycle as 12,000 'years of the gods', which the Puranas and astronomical texts reckon as 4,320,000 human years; a thousand such cycles make one day of Brahma.

The Hindu Calendar
Twelve lunar months, six seasons and the eras that count the years
The Hindu calendar is lunisolar: its months follow the Moon, while an extra month (Adhik Maas) is added roughly every 32 to 33 months to keep it in step with the Sun and the seasons. The year has twelve months from Chaitra to Phalguna and six ritus, and years are counted in eras such as Vikram Samvat (from 57 BCE) and Shaka Samvat (from 78 CE).
Navagraha: The Nine Grahas
Sun, Moon, five planets and the shadow grahas Rahu and Ketu, with Vyasa's hymn
The Navagraha are the nine 'grahas' honoured in Hindu tradition: Surya, Chandra, Mangala, Budha, Brihaspati, Shukra, Shani, and the two lunar nodes Rahu and Ketu. They give their names to the weekdays, are worshipped together in temple shrines, and are invoked through hymns such as the Navagraha Stotram attributed to Vyasa.
Om (Pranava)
The sacred syllable, its meaning in the Mandukya Upanishad, and how to chant it
Om (also written Aum) is the most sacred sound in Hindu tradition, called the Pranava. The Mandukya Upanishad declares that 'all this is Om': its three sounds A, U and M stand for waking, dreaming and deep sleep, and the silence after it for Turiya, pure consciousness. Om begins prayers and mantras, and is chanted slowly with attention to its meaning.
Panchang Explained
The five limbs of the Hindu almanac: tithi, vaar, nakshatra, yoga and karana
A panchang (Sanskrit pañcāṅga, 'five limbs') is the traditional Hindu almanac. For every day it records five things: the tithi (lunar day), vaar (weekday), nakshatra (the Moon's star), yoga and karana, all worked out from the positions of the Sun and the Moon. Families use it to fix festivals, fasts and auspicious times (muhurat).

The Six Darshanas
Six classical ways of seeing truth: Nyaya, Vaisheshika, Samkhya, Yoga, Mimamsa and Vedanta
The six darshanas are the classical orthodox (astika) schools of Hindu philosophy: Nyaya, Vaisheshika, Samkhya, Yoga, Mimamsa and Vedanta. Each accepts the authority of the Vedas but asks different questions, about logic, the nature of matter, consciousness, spiritual practice, ritual duty and the ultimate reality, Brahman. Vedanta itself branched into Advaita, Vishishtadvaita, Dvaita and other schools.