Explanation of the different Mudras (handgestures) expressed in   Buddha statues
Mudras are a non-verbal mode of communication and self-expression, consisting of hand gestures and finger-postures. They are symbolic signs and are used to evoke in the mind ideas symbolizing divine powers or the deities themselves.
The composition of a mudra is based on certain movements of the fingers; in other words, they constitute a highly stylized form of gestureal communication. It is an external expression of 'inner resolve', suggesting that such non-verbal communications are more powerful than the spoken word.
Another interesting meaning is the idea of the mudra that it reveals the secret imbibes in the five fingers. In such an interpretation, each of the fingers, starting with the thumb, is identified with one of the five elements, namely the sky, wind, fire, water, and the earth. Their contact with each other symbolizes the synthesis of these elements, significant because every form in this universe is said to be composed of a unique combination of these elements. This contact between the various elements creates conditions favorable for the presence of the deity at rites performed for securing some desired object or benefit.

• Dharmachakra mudra  - Gesture of preaching the Dharma
• Bumisparsa mudra  - Gesture of the taking the earth as witness by the Buddha
• Dhyana  Mudra-or Samadhi Mudra Gesture of meditation and concentration
• Abhaya Mudra -  Gesture to assuage fear
• Varada mudra - Gesture to welcome or to make offering  
• Vitarka mudra  - Gesture of reasoning
• Anjali mudra- Gesture of offering and veneration  

Dharmachakra Mudra
Dharmacakra mudra (Gesture of preaching the Dharma) 

• This is the position of the "turning of the wheel of Dharma."
• It symbolises one of the most important moments in the life of the Buddha, the occasion when He preached to his former companions the first sermon after His Enlightenment, in the Deer Park at Sarnath.
• Generally reserved for the images of Gautama Buddha
• Position of the Dharmacakra mudra – two hands placed together in front of the breast,  with the right palm forward and the left palm upward or facing the breast, the separated fingers of one of the hands nearly touching those of the other hand.

Bhumisparsha Mudra translates into 'touching the earth'. It is more commonly known as the 'earth witness' mudra. . Bumiparsa mudra (Gesture of the taking the earth as witness by the Buddha) 

• This mudra literally means "gesture of touching the earth"
• Portrays the Buddha taking the earth as witness
• Symbol of unshakeable faith and resolution 
• Describes the moment in life of Gautama Buddha when, armed with his resolve to remain seated under the Bodhi tree until he has solved the problem of the cessation of suffering, he took the earth as testimony of the merits that he had accumulated during his previous births.
• Typical of the representation of the historical Buddha – Buddha seated in the lotus position, the right hand touches the ground with the finger tips near the right knee, all the fingers extended, or only with the tip of the forefinger, while the left hand rests, palm upwards, in the hollow of the thighs.

 Dhyana mudra or Samadhi Mudra

• Mudra of meditation and concentration and of attainment of spiritual perfection.
• Assumed to be the mudra the Buddha adopted when meditating and reaching enlightment under the Pipal tree.
• Gesture also adopted since time immemorial by yogis during concentration and mediation excercises.
• Indicated perfect balance of thought , rest of senses and tranquility.
• may be made with one or both hands. When made with a single hand the left one is placed in the lap, while the right may be engaged elsewhere. The left hand making the Dhyana mudra in such cases symbolizes the female left-hand principle of wisdom. Ritual objects such as a text, or more commonly an alms bowl symbolizing renunciation, may be placed in the open palm of this left hand.
• When made with both hands, the hands are generally held at the level of the stomach or on the thighs. The right hand is placed above the left, with the palms facing upwards, and the fingers extended. In some cases the thumbs of the two hands may touch at the tips, thus forming a mystic triangle.
• Position of the Samadhi mudra with the joined thumbs forming a triangle is symbolic of the Tiratana (Three Jewels) namely the Buddha, Dharma and Sangha. The triangular form also indicates the firmness of the body and of the mind.
•  

Abhaya Mudra (Gesture to assuage fear) 

• Symbolises protection, benevolence and peace, and the dispelling of fear
• Generally made with right hand raised to shoulder height, the arm crooked, the palm of the hand facing outward, the fingers upright and joined
• This mudra – appears to be a natural gesture, probably used in prehistoric times as a sign of good intentions
• The hands raised and unarmed proposes friendship, or peace
• Traditional Indian gesture of appeasement made by the Buddha when. He was attacked by an angry elephant, which immediately calmed the animal.

Varada Mudra ( Gesture of Charity and Compassion)

The hand lowered with the palm facing outward is the gesture of bestowing blessings or of giving charity. The hand is extended downward, palm out. Mostly on standing Buddha images, but sometimes also represented in the sitting position.  

• Mudra offering, giving, welcome, charity, compassion and sincerity
• It is the mudra of the accomplishment of the wish to devote oneself to human salvation
• It is nearly always made with the left hand
• Various variant of the Varada Mudra:

• Rarely used alone, usually in combination with another mudra made with the right hand often Abhaya.
•  

Vitarka Mudra (Gesture of reasoning and Teaching )-

The hand is held closer to the chest than in the Abhaya Mudra. The palm is facing outward. A circle is made with the index finger and the thumb. The other three fingers point upward. Initially made with the right hand, later on the gesture is often portrayed with both hands
Sometimes also substituted for the Dharmachakra Mudra

• Sometimes called "mudra of explanation"  
• This mudra is made with both hands in Abhaya and Varada, but with the thumbs touching the tips of the forefingers.
• Symbolises one of the phases of the teaching of the Buddha, that of discussion or dispensation of the Dharma.
• This is the mudra that convinces listeners and leads them to conversion or enlightenment.
• Various variant of the mudra:

• Thumb may not completely touch the forefinger, or it may extend beyond it on the side

Anjali mudra (Mudra of offering and veneration) Namaskara Mudra 

• Made with two hands joined vertically in front of the chest, as in the attitude of prayer.
• Evokes an offering of good feelings of one towards another
• Also indicates veneration if it is made at the level of the face

This mudra is reserved for praying figures – which often accompany a statue of the Buddha in the art of India or South East Asia.