KALPA is one of the six branches of knowledge (Vedāṅgas) emerging from Vedas and deals with domestic and other rituals.

Vedāṅgas are mentioned first in Muṅḍakopaniṣad, the upaniṣad for those who are renouncers.

The first khaṅḍa of Muṅḍakopaniṣad contains the following verses:

१.ब्रह्मा देवानां प्रथमः संबभूव विश्वस्य कर्ता भुवनस्य गोप्ता ।
  स ब्रह्मविद्यां सर्वविद्याप्रतिष्ठामथर्वाय ज्येष्ठपुत्राय प्राह ॥

1. The first among Gods, Brahma the maker of the universe
    Protector of the earth came into being
    He taught Brahmavidya, the basis of all knowledge
    To his eldest son, Atharva

२. अथर्वणे यां प्रवदेत ब्रह्माथर्वां तां पुरोवाचङ्गिरे ब्रह्मविद्याम् ।
   स भारद्वाजाय सत्यवहाय प्राह भारद्वाजोऽङ्गिरसे परावराम् ॥

2. What was taught by Brahma to Atharva
    Atharva of old taught to Aṅgira
    He taught Bhāradvāja Satyavaha
    Bhāradvāja taught Aṅgirasa the higher and lower knowledge

 
३.शौनको ह वै महाशालोऽङ्गिरसं विधिवदुपसन्न पप्रच्छ ।
  कस्मिन्नु भगवो विज्ञाते सर्वमिदं विज्ञातं भवतीति ॥

3. Śaunaka, the great householder respectfully asked Aṅgirasa
    What must one know to know Brahmavidya?

 
४.तस्मै स होवाच ।
  द्वे विद्ये वेदितव्ये इति ह स्म यद्ब्रह्मविदो वदन्ति परा चैवापरा च ॥

4. He answered: Those who know Brahmavidya say that there are two types of knowledge - Higher and Lower.

५.तत्रापरा ऋग्वेदो यजुर्वेदः सामवेदोऽथर्ववेदः ।
  शिक्षा कल्पो व्याकरणं निरुक्तं छन्दो ज्योतिषमिति ।
  अथ परा यया तदक्षरमधिगम्यते ॥

5.  In it, the lower is the Ṛg Veda, Yajur Veda, Sāma Veda and Atharva Veda-
    Śikśa, Kalpa, Vyākaraṇa, Nirukta, Chaṅdas and Jyotiṣa
    But the higher is that by which the imperishable(akṣara) is understood

Vedāṅgas, the six limbs of Vedas represent different branches of knowledge.

Śikśa: Phonetics
Vyākaraṇa: Grammar
Nirukta: Etymology
Chaṅdas: Prosody metre
Jyotiṣa: Astronomy
Kalpa: Rituals

Kalpa is the aṅga of knowledge of rituals that are prescribed for practice. It is called the Kara or the hand of the Vedas. While other aṅgas represent knowledge, Kalpa represents activity to be carried out.

छन्दः पादौ शब्दशास्त्रं च वक्त्रं कल्पं पाणी ज्योतिषं चक्षुषी च ।
शिक्षा घ्राणं श्रोत्रमुक्तं निरुक्तं वेदस्याङ्गान्याहुतानि षड् हि ॥

Chaṅdas  is represented by feet, Śabdaśāstram(Vyākaraṇa) by the face
Kalpa by hand and Jyotiṣa by eyes
Śikśa is represented by the tongue Nirukta by speech
These are the six parts of Vedas

(Beginning śloka of Ṛksarvaa)

Kalpa is represented by Kalpa sūtras (aphorisms) written by various Ṛṣis belonging to the four  Vedas and their branches.

Kalpa Sūtras are of four kinds:

Śrauta Sūtras: Rituals such as Yagas, Yajñas performed as per Vedic prescription.
Gṛhya Sūtras: Rituals to be observed by the house holder
Dharma Sūtras: Laws to guide the behaviour of all sections of people
Śulba Sūtras: Guide lines for preparing sacrificial Homa Kunḍas

The following are the currently available Kalpa Sūtras while many texts are understood to have been lost.

Śrauta Sūtras:

Gṛhya Sūtras:

Dharma Sūtras:

Śulba Sūtras: All the Śulba Sūtras belong to Yajur Veda.

Śrauta Sūtras

Śrauta sacrifices are classified into two categories:

1. Haviryajñas
2. Somayajñas

There are seven Haviryajñas and seven Somayajñas

Haviryajñas:
1. अग्न्याधान (Agnyadhana) 
2. अग्निहोत्र (Agnihotra) 
3. दर्शपूर्णमास (Darśapūrṇamāsa)
4. आग्रयण (Āgrayaṇa)
5. चातुर्मास्य (Cāturmāsya) 
6. निरूढपशुबन्ध  (Niruḍhapaśubandha)
7. सौत्रामणि (Sautrāmaṇi)

Somayajñas:

1. अग्निष्टोम (Agnishtoma)
2. अत्यग्निष्टोम (Atyagnisthoma)
3. उक्थ्यः  (Ukthya:)
4. षोडशी (Ṣoḍaṣi)
5. वाजपेयः (Vājapeya) 
6. अतिरात्रः (Atiratra)  
7. आप्तोर्यामः (Āptoryama:)

Śrauta yajñas are conducted as specified in the Śrutis namely, the Vedas. They are therefore called Vedic rites. These are conducted over periods of varying durations. Offerings of different materials are made to propitiate Gods for success in achieving different goals.

Apart from the fourteen Śrauta yajñas, there are five yajñas called pancha mahāyajñas to be observed by the householder daily in gṛhastāśrama.

These are
1. Deva yajña
2. Pitṛ yajña
3. Bhūta Yajña
4. Manuṣya yajña and
5. Brahma yajña

They are also called
1. Huta
2. Ahuta
3. Prahuta
4. Brahmyahuta and
5. Praśῑta

These are elaborated in Gṛhya sūtras.

Gṛhya Sūtras:

Gṛhya sūtras contain directions for various dhārmic duties to be observed by the householder.

Dharma Sūtras:

Dharma Sūtras not only deal with the ‘law’ or righteousness but also on the broader issues of the conduct of men, secular law (Vyavahāra) and duties of the king (rāja-dharma). Dharma sūtras followed by other Smṛiti texts were the earliest law books known to mankind.

Śulba Sūtras:

Śulba Sūtras (Śulba means "string, cord, rope") are sūtra texts containing geometrical specifications related to construction of Homa Kuṅḍas (Altars).

It is the considered opinion that because of the specifications of intricate shapes of the Altars, Śulba sūtras laid the foundation for mathematics, especially geometry.
The concept of the Pythagoras theorem was known to the authors of Śulba sūtras. Square roots, numerals, conversion of square shapes into circular shapes of the same area etc. were known.

Different shapes of Homa Kuṅḍas such as the falcon, tortoise, rhombus etc. were prescribed with mathematical formulae to conduct yajñas to achieve desired goals of different types.

People in the Vedic period firmly believed that their fortunes were not in their hands and that it was essential to please the Gods by conducting yajñas and making offerings.

At the same time the scriptures also enjoined them to lead a disciplined life and make efforts to realise the ultimate as elaborated in the puruśārthas namely, Dharma, Artha, Kāma and Mokṣa.