PURUSHOTTAM MAS (Adhik Mas)

The Hindu calendar is lunar based, unlike the Gregorian (Western) which is solar based. Since the lunar based calendar lags slightly, an intercalary month is added approximately every 2.5 years. This is known as Adhik (extra) mas. It is considered even more auspicious than Shravan.
The lunar month in which the sun does not transmigrate clearly, is called Adhik Mas or Purushottam Mas – additional month.
There are several kathas related about the glory of Purushottam Mas in the Narad Puran
In ancient times, the rishis Asit, Deval, Angira, Vamdev and others gathered at Naimisharanya Kshetra. Soon Sutpurani too arrived, while on a pilgrimage. Welcoming him, the others requested him to do katha which would imbue moksha.
Sutji replied, "Once Naradji visited Nar-Narayan rishi's ashram. He humbly prayed, "O Prabhu! What is the way to moksha in this KaliYuga - age of darkness, which is plunging in ever increasing hedonism?"
The rishi replied, "O Muni! If man was to listen to the divine lila of Purushottam Narayan, then even in Kali Yuga, He will grant moksha."
Therefore the rishis listened to the lila in Adhik Mas, henceforth also known as Purushottam Mas.

There are other similar stories in the Padma Puran extolling Purushottam Mas's glory.

Rituals

In this month, devotees awaken at brahma muhurt – around 4.30 a.m. After the ritual; ablutions, they perform puja.
They should do pranayam for physical and mental purity. If circumstances are favourable, devotees should offer shodshopchar puja – worship with sixteen different types of pujadravya, materials for puja.
Those with robust health should do farar or ektana – one meal a day. One should listen to katha with bhaktibhav.
The merit of this vrat is greater than that of performing a hundred yagnas, since this leads to attainment of Paramatma’s abode (Bruhad Naradiya Puran 22-23).
Bhagwan Swaminarayan has also enjoined the observance of Purushottam Mas by offering special devotion. The unparalleled feature of this month is that each tithi – date of this month celebrates a sacred festival which falls on that tithi during the year.
Hindus worldwide celebrate this sacred month, which arrives every thirty-two months, by performing extra malas, pradakshinas, pilgrimages, scriptural reading and parayans - holding a katha series of a sacred text.

Source - kids.baps.org

GURU POORNIMA

Guru Poornima is an Indian festival that is celebrated as per the Hindu Moon Sign calendar to express reverence towards your Guru, your teacher or mentors. It falls on the day of the full moon or Poornima of Ashadh month. Etymologically, the word Guru has been derived from two parts – Gu that means darkness and Ru that is the antidote to the darkness. Naturally, the word Guru implies someone who shows takes us away from the darkness of ignorance to the light of knowledge.

There is a Shloka that states -
Agyan timirandhasya gyananjan shalakaya
chakshurunmilitam yen tasmai shri gurave namah

Gurur Brahma, Gurur Vishnuhu, Guru Devo Maheswaraha
Guru Saakshaat Parabhrahma, Tasmai Sri Gurve Namah

Traditionally the festival is celebrated by Buddhists in the honor the lord Buddha who gave His first sermon on this day at Sarnath, Uttar Pradesh, India. While Hindus celebrate it in the honour of the great sage Vyasa, who is seen as one of the greatest gurus in ancient Hindu traditions, and a symbol of the Guru-shishya tradition.

Vyasa was not only believed to have been born on this day, but also to have started writing the Brahma Sutras on ashadha sudha padyami which ends on this day, hence their recitations as a dedication to him, are organised on this day, which is also known as Vyasa Purnima.
The festival is common to all spiritual traditions in Hinduism, where it is dedicated to the expression of gratitude towards the teacher by his/her disciple.

Hindu ascetics and wandering monks (sanyasis), observe this day by offering puja to the Guru, during the Chaturmas, a four month period during the rainy season, when they choose seclusion, and halt at one selected place; some also give discourses to the local public. Students of the Indian classical music, which also follows the Guru shishya parampara, celebrate this festival.

SOURCE: Wiki and Hindu blog.
Image - Google