Deities, holy being: The Goddess
Some scholars suggest that before the Indo-Aryan invasion (1300 BCE), from which Hinduism sprouted, the former Indus Valley civilization had a cult of the Great Mother or the Divine Mother, similar to such cults in Persia, Asia Minor and the Mediterranean. In present Hinduisms, this general idea of this deity is expressed with the term Devi.
Devi, or the divine feminine as an equal counterpart to the divine masculine, manifests herself in various ways, from the benevolent aspect of gentle wife and amorous mother, to  fierce warrior, to even the personification of Death itself. Let's see three example:

Durga
In the Hindus pantheon, Durga is one of the most popular goddesses. She is the goddess of victory of Good over Evil and her creation takes place in the context of a cosmic crisis. The demons were on the ascent, and they had become a threat to cosmic stability. The male gods were unable to contain and subdue them. A number of male gods having failed to resist the invasion, assembled into a conclave and emitted their energies together which took the form of the warrior goddess, Durga, the invincible.

Lakshmi/Parvati
The Devi soon became associated (around 400 BCE) with Supreme Gods like Vishnu (with the name of Lakshmi) and Shiva (with the name of Parvati), and emerged as wife or consort, acquiring - addition to her earlier attributes - characteristics of a gentle mother and model wife.

Kali
She is the fiercest (and most commonly known) aspect of the goddess. The name of Kali means "Time" or "Death" Hence, Kali is the Goddess of Time and Change. She represents death, destruction, and the consuming aspects of reality, the inevitable counterpart of the generative aspect of life, represented by other manifestations of the Devi.

Main doctrinal traditions: Shaktism or Devi worship traditions
Shaktism is a denomination of Hinduism that focuses worship upon the Devi as the Ishvara, the Supreme God. It is one of the primary schools of devotional Hinduism.
Shaktism (see the terms Shakti below) regards Devi as the Brahman itself, the Absolute, with all other forms of divinity, female or male, considered to be merely her diverse manifestations.
The beginnings of Shaktism are shrouded in the mists of prehistory, being the earliest Mother Goddess figurine unearthed in India, belonging to the Upper Paleolithic, dated to approximately 20,000 BCE
The most central and pivotal text in Shaktism is the Devi Mahatmya (Glory of the Goddes), composed some 1,600 years ago. Here, for the first time, the various mythic, cultic and theological elements relating to diverse female divinities were brought together in a somehow crystallized tradition. Devi traditions, especially when she is revered in the form of Kali, are characterized by Tantric practices (see below).

Main doctrinal tenets: the concept of Supreme God or Ishvara
Hinduism is commonly said to be a polytheistic religiosity, but it should be understood as Henotheism. Henoteism is the belief in and worship of a single god while accepting the existence or possible existence of other deities that may also be worshipped. In the case of Hinduism, a concept of pivotal importance is that of Ishvara (the Lord). The Supreme God is thus the personification of Brahman, the eternal ground of reality, which is behind a world in cyclical flux of birth, development and destruction. Because of this, Ishvara is different from the other deities, which, although being superior to men, are nonetheless subject to Samsara and Karman (the cycle of reincarnation and the law of deeds' retribution).
Hinduism could be called polytheistic in the sense that there are many different gods—classically there are said to be 330 million! But Hindus often worship a particular form of the god or goddess as the Supreme God, which is also called an Ishtadevata, a chosen or personal god. Some of these forms are pan-Indian, such as Vishnu or Shiva, while others are local, often only known at the regional level.

Main doctrinal tenets : the concept of Shakti
On a more philosophical level Devi is synonymous with Shakti, the impersonal female aspect of the divine. This term means "Power" or "empowerment". As the various manifestation of the Devi explained above show, Shakti refers to the dynamic, active, generative (but also destructive) forces that moves and changes the phenomenal world. Shakti is the female, active counterpart without which the male aspect, generally passive, remains impotent and void.
Not only is Shakti responsible for creation, it is also the agent of all change. Shakti is cosmic existence as well as means of liberation, its most significant form being the Kundalini Shakti, a mysterious force, often depicted like a snake coiled in the abdomen of the practitioner.
This idea of shakti is pivotal in Tantric traditions (see below).

Main doctrinal traditions & main rites: Tantrism
Tantrism is the name given by scholars to a style of meditation and ritual which arose in India no later than the 5th century CE. It is a inter-sectary religious phenomena so pervasive that virtually any religious traditions in India could have its Tantric version.
Tantrism derive its name from a corpus of texts called Tantra (see below). Although it should be better understood as a set of ritual practices, there is nonetheless a common religious worldview beneath the variety of ritual prescriptions: the Tantric Hindus traditions consider that before the creation of everything there was the Absolute as the union of male aspect (the passive and transcendent ) and female aspect (active and immanent). Then a break occurred and the world came to being. The religious goal of the practitioner is to re-estabilish this primordial unity.
The ordinary physical world is not considered illusory, on the contrary, it is thought to be imbued with the Shakti (see above), the female creative force. The practitioner then is expected to control this energy by means of rituals that imply an active use of the body, voice and senses. This is in contrast with the more ascetic-style of other non-tantric traditions.
Because of such  control of this force, Tantric practice is also claimed to be far more powerful than ordinary religious practice. It is also widely believed that Tantric spiritual attainments include superhuman powers as a natural byproduct. Aspirants are discouraged from seeking such powers, but this belief has often pushed monarchs to sponsor Tantric monasteries.
There's a type of Tantric meditation in which the human body is considered as a microcosmic equivalent of the world that, as said before, came to being thanks to the separation of the male and female principles. In this meditation the Shakti is called Kundalini and it is depicted like a snake coiled in the abdomen of the practitioner. The goals is to awake this energy and make it flow vertically in order to unite with the male passive principle that is thought to reside beyond the head. Thus the practitioner creates inside of him/her the primordial unity.
 

Sacred texts and other main texts: Tantra
Tantra are texts composed around the5h and 10th cen. CE. They are rather obscure texts, dealing mainly with ritual prescriptions and practices of meditation. The contents of these texts is considered esoteric, that is, only through the mediation of a master a practitioner can understand the symbolism implied in the various rituals. This secrecy serves two functions. On one hand, it conceals the rites and practices from the uninitiated, seen as unqualified to receive it. On the other, it creates an exclusive sub-community with a well-defined sense of identity.

Analysis of Sources
Source n° 1
The three representations of the manifestation of the Devi:
First Image, Durga: The Goddess is depicted in the upper right, on the background, while the foreground is occupied by the corpse of the slayed demon chief. On the upper left various gods are adoring Durga for having defeated the demons. Among them there are Ganesha, with the elephant head, Shiva, with the cobra snake around his neck; Vishu, with a crown emitting light, Brahma with the four bearded heads.
This image is a illustration for a copy of the main religious text about the Godddes, the Devi Mahatmya (Glory of the Goddes).

Second Image, Parvati
The Goddess here is the gentle wife Parvati assisting Shiva in meditation. Shiva is identifiable by the cobra around his neck and by the crescent moon pendant on his crest.

Second Image, Kali
The Goddess here is depicted as the fierce Kali, the unstoppable Time/Change/Death, to whom even the other gods must pay homage. The three other Gods are Vishnu (identifiable by the blu-purple skin and by the crown), Shiva (identifiable by the trident) and Brahma (identifiable by the four head).
The corpses under Kali are not sacrificial victims, instead they represent the devotees, who completely abandon themselves to the deity and accept the inevitability of change and death.

Source n° 1
This image show an example of an androgynous deity which is considered in Tantrism to be the primordial origin of All. In this case, the deity identifiable with Shiva (who is therefore unite with his wife Parvati) because of the trident on his right arm. The androgyny is reveled by the upper body of the deity, which has one breast and a slightly wider hip on his left side.

Intercultural & Interdisciplinary information.

Buddhism I. Brief Overview sec. 7
Daoism  sec.2
Islam II Themes p.1