As you have asked about the course outline of the Design and Analysis of Algorithms subject of the Indian Institute of technology (IIT) Bombay, I am providing you with it, check below for the details

Overview of the course
Framework for Algorithms Analysis
Algorithms Analysis Framework - II
Asymptotic Notations
Algorithm Design Techniques : Basics
Divide And Conquer-I
Divide And Conquer -II Median Finding
Divide And Conquer -III Surfing Lower Bounds
Divide And Conquer -IV Closest Pair
Greedy Algorithms -I
Greedy Algorithms - II
Greedy Algorithms - III
Greedy Algorithms - IV
Pattern Matching - I
Pattern Matching - II
Combinational Search and Optimization I
Combinational Search and Optimization II
Dynamic Programming
Longest Common Subsequences
Matrix Chain Multiplication
Scheduling with Startup and Holding Costs
Average case Analysis of Quicksort
Bipartite Maximum Matching
Lower Bounds for Sorting
Element Distinctness Lower Bounds
NP-Completeness-I -Motivation
NP - Completeness - II
NP-Completeness - III
NP-Completeness - IV
NP-Completeness - V
NP-Completeness - VI
Approximation Algorithms
Approximation Algorithms
Approximation Algorithms for NP