IIT Bombay was established in 1958 as a second-oldest institute of the Indian Institutes of Technology system.

As you asking I am telling IIT Bombay offered PhD in following department

Aerospace Engineering (AE)
[Department of Aerospace Engineering]
Biosciences and Bioengineering (BB)
[Department of Biosciences and Bioengineering]
Chemical Engineering (CL)
[Department of Chemical Engineering]
Chemistry (CH)
[Department of Chemistry]
Civil Engineering (CE)
[Department of Civil Engineering]
Climate Studies (CM)
[Interdisciplinary Group in Climate Studies]
Computer Science and Engineering (CS)
[Department of Computer Science and Engineering]
Design (ID)
[Industrial Design Centre (IDC)]
Earth Sciences (ES)
[Department of Earth Sciences]
Educational Technology (ET)
[Interdisciplinary Group in Educational Technology]
Electrical Engineering (EE)
[Department of Electrical Engineering]
Energy Science & Engineering (EN)
[Department of Energy Science & Engineering]
Environmental Science and Engineering (EV)
[Centre for Environmental Science & Engineering](CESE)
Geoinformatics & Natural Resources Engineering)(GNR)
[Centre of Studies in Resources Engineering (CSRE)]
Humanities and Social Sciences (HSS)
[Department of Humanities and Social Sciences]
Industrial Engineering & Operations Research (IO)
[Interdisciplinary Group in Industrial Engineering & Operations Research]
Management (MG)
[Shailesh J. Mehta School of Management]
Mathematics (MA)
[Department of Mathematics]

Mechanical Engineering (ME)
[Department of Mechanical Engineering]
Metallurgical Engineering and Materials Science (MM)
[Department of Metallurgical Engineering and Materials Science]
Nanotechnology & Science (NT)
[Centre for Research in Nanotechnology & Science (CRNTS)]
Physics (PH)
[Department of Physics]
Systems & Control Engineering (SC)
[Interdisciplinary Group in Systems & Control Engineering]
Technology and Development (TD)
[Centre for Technology Alternatives for Rural Areas(CTARA)]
Urban Science & Engineering (US)
[Centre for Urban Science & Engineering (CUSE)]
APPENDICES
Fees and Deposits
Sponsorship letter for fulltime candidates
Employer’s Letter in case of candidates joining Ph.D. programme on Study Leave
Sponsorship Certificate for External Registration
No Objection Certificate for College Teacher
Statement of Purpose for Ph.D. Application (SoP)



Address
Indian Institute of Technology, Bombay
Powai
City : Mumbai
State : Maharashtra
Country : India
Contact No : 022-25722545
Contact Email : dean.aa@iitb.ac.in