Dr. Sachidanand Sinha was the first president of the Constituent Assembly

Constitution of India Wikipedia History
The Cabinet Mission
World War II in Europe came to an end on May 9, 1945. In July, a new government came to power in the United Kingdom. The new British government announced its Indian Policy and decided to convene a constitution drafting body. Three British cabinet ministers were sent to find a solution to the question of India's independence. This team of ministers was called the Cabinet Mission.
The Cabinet Mission discussed the framework of the constitution and laid down in some detail the procedure to be followed by the constitution drafting body. Elections for the 296 seats assigned to the British Indian provinces were completed by July-August 1946. With the independence of India on August 15, 1947, the Constituent Assembly became a fully sovereign body. The Assembly began work on 9 December 1947.

The Constituent Assembly
The Constituent Assembly was the body that framed the constitution of India. The people of India elected the members of the provincial assemblies, who in turn elected the constituent assembly. Rajendra Prasad, Sardar Patel, Maulana Abul Kalam Azad and Shyama Prasad Mukherjee were some important figures in the Assembly. There were more than 30 members of the scheduled classes. Frank Anthony represented the Anglo-Indian community, and the Parsis were represented by H.P. Modi. The Chairman of the Minorities Committee was Harendra Coomar Mookerjee, a distinguished Christian who represented all Christians other than Anglo-Indians. Constitutional experts like Alladi Krishnaswamy Iyer, B.R. Ambedkar, B.N. Rau and K.M. Munshi were also members of the Assembly. Sarojini Naidu and Vijaylakshmi Pandit were important women members.
Dr. Sachidanand Sinha was the first president of the Constituent Assembly. Later, Dr.Rajendra Prasad was elected president of the Constituent Assembly while B.R. Ambedkar was appointed the Chairman of the Drafting Committee.

Features
The Constitution of India draws extensively from Western legal traditions in its enunciation of the principles of liberal democracy. It is distinguished from many Western constitutions, however, in its elaboration of principles reflecting aspirations to end the inequities of traditional social relations and enhance the social welfare of the population. According to constitutional scholar Granville Austin, probably no other nation's constitution "has provided so much impetus toward changing and rebuilding society for the common good." Since its enactment, the constitution has fostered a steady concentration of power in the hands of the central government - especially the Office of the Prime Minister. This centralization has occurred in the face of the increasing assertiveness of an array of ethnic and caste groups across Indian society. Increasingly, the government has responded to the resulting tensions by resorting to the formidable array of authoritarian powers provided by the Constitution. However, a new assertiveness shown by the Supreme Court and the Election Commission suggests that the remaining checks and balances among the country's political institutions are resilient and capable of supporting Indian democracy. Furthermore regional parties are gaining popularity at the expense of national parties which has led to coalition governments at the centre. As a consequence, power is becoming more decentralised.
The Constitution in its final form owes much to a number of different principles from various other Constitutions. The general structure of the Constitution's democratic framework was largely the work of B. N. Rau, a constitutional scholar of international standing. Supporters of independent India's founding father, Mohandas K. Gandhi, backed measures that would form a decentralized polity with strong local government — known as panchayat — in a system known as Panchayati Raj, i.e. rule by Panchayats. However, the view of more modernist leaders such as Jawaharlal Nehru, ultimately prevailed leading to the establishment of a parliamentary system of government and a federal system with a strong central government.

Features of the Indian Constitution adapted from other Constitutions
British Constitution
Parliamentary form of government
The idea of single citizenship
The idea of the Rule of law
Institution of Speaker and his role
Lawmaking procedure
Procedure established by Law u/a 13
United States Constitution
Charter of Fundamental Rights, which is similar to the United States Bill of Rights
Federal structure of government
Power of Judicial Review and independence of the judiciary
President as supreme commander of armed forces u/a 52
Due process of law u/a 13
Irish Constitution
Constitutional enunciation of the directive principles of state policy
French Constitution
Ideals of Liberty, Equality and Fraternity
Canadian Constitution
A quasi-federal form of government (a federal system with a strong central government)
The idea of Residual Powers
Australian Constitution
Freedom of trade and commerce within the country and between the states
Power of the national legislature to make laws for implementing treaties, even on matters outside normal Federal jurisdiction
Japanese Constitution
Fundamental Duties u/a 51-A
Weimar Constitution
Emergency Provision u/a 356

Criticisms
The Constitution of India differs from other western constitutions, from which it has derived inspiration, in the fact that it stipulates the supremacy of the legislature as the supreme law making body of the land. In that respect, it renders the legislative arm of government nominally more powerful than either the executive or the Judiciary. It is also widely criticised that although the underlying constitution is very sound, it has provided scope for misuse by people in power and its executive which is evident from the prevailing corruption and red tape in the country.