Pivotal events for the tradition: Diffusion in Tibet

Tibetan Buddhism, also called (incorrectly) Lamaism, is a branch of Vajrayana (Tantric, or Esoteric) Buddhism that evolved from the 7th century CE in Tibet. Its complex Tantric ritual practices involve an active use of the body, the voice and the senses. (see more on Buddhism Module I sec. 7). Moreover a complex system of correspondences between ritual practices, ritual instruments and doctrinal tenets is one of the main features of Vajrayana Tibetan Buddhism. Tibetan Buddhism also incorporates the monastic disciplines of early   Buddhism and the shamanistic features of the indigenous Tibetan religion, Bon.
Other characteristic of Tibetan Buddhism are: the unusually large segment of the population actively engaged in religious pursuits (up until the Chinese communist takeover of the country in the 1950s an estimated one-quarter of the inhabitants were members of religious orders); its system of “reincarnating lamas”; the traditional merger of the spiritual and temporal authority in the office and person of the Dalai Lama; and the vast number of divine beings  which are considered at the same time deities and symbolic representations of the psychic life.
When Tibet was converted to Buddhism (7th to 11th century), the most dynamic form in India was Vajrayana ; thus, it was this tradition that became established. Little is known about the early stages of the conversion (7th to 9th century). Several Tibetan schools that developed during the 11th and 12th centuries traced their lineage back several centuries to particular Indian saints.
By the 14th century the Tibetans had succeeded in translating all available Buddhist literature in India and Tibet; many Sanskrit texts that have since been lost in the country of their origin are known only from their Tibetan translations that form the so called Tibetan Canon.
From a political viewpoint, only in Tibet did Buddhists establish a theocratic polity that lasted for an extended period of time. Beginning in the 12th century, Tibetan monastic groups forged relationships with the powerful Mongol rulers that often gave them control of governmental affairs. In the 17th century the Gelug school,  commonly known as the Yellow Hats, the order of the Dalai Lamas, working with the Mongols, established a monastic regime that was able to maintain almost continual control until the Chinese occupation in the 1950s.
Just to be clear the Dalai Lama is not, as commonly Known, the leader of Buddhist all over the word. Nor it represents the leader of all Tibetan Buddhism. The Dalai Lama is the head monk of the Gelug school of Tibetan Buddhism,  The 14th and current Dalai Lama is Tenzin Gyatso, recognized since 1950.
The Dalai Lama is traditionally thought to be the successor in a line of masters who are considered to be metaphorical manifestations of Avalokiteśvara, the Bodhisattva of Compassion (see also Buddhism Module I sec. 6). The name Dalai Lama is a combination of the Mongolic word "dalai" meaning "ocean" and the Tibetan word "lama" meaning "guru, teacher, mentor". The Tibetan word "lama" corresponds to the better known Sanskrit word "guru" (see also sec. 6 and Hinduism Module sec. 11)
In the second half of the 20th century Tibetan Buddhism spread to the West, particularly after the subjugation of Tibet to Chinese Communist rule sent many refugees, including highly regarded “reincarnated lamas,” out of their homeland. Tibetan religious groups in the West include both communities of refugees and those consisting largely of Westerners drawn to the Tibetan tradition. See also sec. 6 of this Module

Source Analysis

Source 1:

see above Pivotal events for the tradition: Diffusion in Tibet

Source 2:

Sand Mandala

A Mandala is a spiritual and ritual symbol of Buddhism (but also in Hinduism) representing the correlation with the Universe (divided in various realms, Buddhas, deities and so on) and the human mind (divided in various state of consciousness, emotion, desires and so on). The basic form of most mandalas is a square with four gates containing a circle with a center point.
Mandalas may be employed for focusing attention of practitioners as a spiritual guidance tool, for establishing a sacred space, and as an aid to meditation and trance induction.
Tibetan Buddhist tradition involves the creation and destruction of Mandalas made from colored sand. A Sand Mandala is ritualistically destroyed once it has been completed in order to symbolize the Buddhist doctrinal belief in the transitory nature of everything.

Source 3:

Vajra, a ritual instrument

The Vajra is essentially a type of club with a ribbed spherical head. The ribs may meet in a ball-shaped top, or they may be separate and end in sharp points with which to stab. The Vajra is used symbolically to represent firmness of spirit and spiritual power. The use of the Vajra as a symbolic and ritual tool spread from India along with Indian religion and culture to other parts of Asia, notably Tibet and Japan.
In the tantric traditions of Buddhism, the Vajra is a symbol for the true nature of reality, Voidness , which is not a negative term, but indicates the endless creativity and potency. The five-pronged Vajra (with four prongs, plus a central one) is the most commonly seen Vajra There is an elaborate system of correspondences between the five prongs and  the Tibetan Buddhist teachings.

Source 4:

Mudras

Mudras were introduced from India into Tibet in the 8th century A.D. They became part of a ritual language, involving the use of Mantras (sacred utterance) Mudras and the thunderbolt scepter or Vajra. For example, a Mantra has first be visualized in mind, then pronounced as sound, and finally expressed physically through hand gestures, or Mudras. Thus, following the Vajrayana Buddhism's teachings, mind, speech and body  are called into activity. Through these the practitioner is thought to reach Enlightenment .
In Mudras each hand and each finger has various particular significance. The right hand, for example, is associated with the moon and male principles. It stands for the Compassion. The left hand is associated with the sun and female principles. It stands for Wisdom . Examples of the various Mudras can be seen also on many Buddhist statue.

An example of the meanings of the three mudras of source n°4 (from up to down)

Intellectual Argument
The gesture of discussion and debate indicates communication and an explanation of the Buddhist Teaching. The tips of the thumb and index finger touch, forming a circle. All other fingers are extended upwards.

Prayer; Adoration; Salutation; Reverence
In India, this gesture indicates salutation and respect. In Buddhist iconography, it symbolizes adoration. If held under the mouth, it indicates homage to the word of the teacher. It is therefore never seen on Buddha himself, as he is the subject of reverence. The two hands joined together also symbolize the static and dynamic. The hands are kept close to the chest in devotional attitude with the palms and fingers pressed together.

Meditation
The highest state of consciousness can be reached by means of deep concentration, tranquility and identification with the supreme unity. This gesture of meditation, made with both hands, or with the left hand alone, indicates deep concentration or absolute balance. Both hands are placed in the lap, right hand on left hand, with all fingers extended and palms facing upward. Thumbs touch each other.