Saraswati the Goddess of music and education

Goddess Lakshmi also called Maha Saraswati. She is Part of Goddesses Trinity with Kali and Laxmi Mata. She is Devi of Education and Music, Knowledge, Art. She is God Brahma's consort. Maa Saraswati worshipped by different names (VANI, VACHI, BRAHMI, BRAHMNI etc.) she is also known as Goddess of Vedas. She is Indian Goddess of Music. Saraswati Mata often seated on white male Swan(Hamsa is sacred bird). She dressed in pure white which means light & SATWA GUNA or Purity. Her four hands holds Pustak(book), Mala(rosary), Veena(musical instrument) sometimes a Water Pot. Saraswati Mata also known as HAMASVAHINI. She is always located near the River. Savitri & Gayatri is also Saraswati's Avatar.

As she holds book this true and Divine Knowledge, Mala represents inner spirituality. She is worshipped in Nepal and Assam also. Saraswati Vandana is a most important mantra for worshipping her some other mantras are "Om Aim Hrim, Kleem Maha Saraswati Deyaya, Namaha", "Vad Vad Vaagwaadinee Swaaha".

Shiva the Destructor in Trinity

Shiva is the Destroyer within the Trimurti.He is destroyer of Evil.Shiv ji has different names Mahadev, Aghori,Yogi, Jtadhari, Neelkanth (have blue neck), Rudra, Aradhanarishvara (half men & half women) Pashupatinath etc. Aghori means he lives simple life on kailash parwat (Mount kailasha) with his wife PARVATI (Sati)and two children GANESHA & KARTIKEYA. Shiva is limitless, unchanged. He is soul of the Universe. The holly river "GANGA" following his matted hair(jtas).He is always dressed in Bhagambar. Shiv ji had Third Eye, it is believe that it opens when shiv ji is angry. Rudra TANDAV (Divine dance)when he is extermly angry. Shiva is NATRAJ (God of dance). Shiva Tandav Stotram described Shivji's anger,beauty and power. 

As Shiv ji also known as "Pashupatinath"(pashu means animal), he is always carry Snake on his neck that represents "Ego" which once controlled can be wore as an ornament. According to Hindu Mythology once snakes approached to lord Shiva for shelter,but due to cold weather on Kailash Pawat snacks used to approach Mahadev's warmth body. Rudra always carry Trishula(Trident) & Damru (musicale instrument) with him."Nandi"(Bull) gate guardian of Shiva. White colour of Nandi represents purity. 

"OM NAMAH SHIVAYE" is main & most important mantra in Hinduism and Shivism.
This Mahamantra represents EARTH,WATER,FIRE,AIR & SKY. Roasary of Rudrakasha is used for chanting this mantra.Shiv ji usually worship in the form of "SHIVLING"(Lingam). Maha Shivrati celebrated in honour of the lord Mahadev."The Great Night of Shiva" means Shivratri. On this night devotees used to visit "Jyotirlingams", and other are keeps awake all night. Shraavan mass (saawan month) is very important in Hinduism, for HINDUS saawan is a month of fasting.This is also shiva's month, Hindus fasting on every Monday to the bhagwan Shiv.

shiva family(shiv parivar)
According to Hindu Myths GANESHA(Ganpati) was restored son of lord shiva & Parvati mata.Famous name of Ganesh is VIGHANHARTA which means remover of obstacles. shri (shree) always added before his name. Ganesha had a elephant face.other name of ganesh is EKDANTA(has one tusk).Ganesha often riding on a MOUSE(rat)."BUDDHI, RIDDHI, SIDDHI" are Ganesha's consort 
KARTIKEYA  worshiped in sout india with name of MURGANA, he is riding on peacoack. He grows up as a Warrior.