Tim Roughgarden's Online Courses
MOOCs on Coursera
Algorithms Specialization
based on Stanford's undergraduate algorithms course (CS161). See also the accompanying Algorithms Illuminated book series.
YouTube playlists are
here and
here.
Comprises four 4week courses:
 Part 1: Divide and Conquer, Sorting and Searching, and Randomized Algorithms
 Covers asymptotic ("Bigoh") notation, sorting and searching, divide and conquer (master method, integer and matrix multiplication, closest pair), and randomized algorithms (QuickSort, contraction algorithm for min cuts).
 Part 2: Graph Search, Shortest Paths, and Data Structures
 Covers data structures (heaps, balanced search trees, hash tables, bloom filters), graph primitives (applications of breadthfirst and depthfirst search, connectivity, shortest paths), and their applications (ranging from deduplication to social network analysis).
 Part 3: Greedy Algorithms, Minimum Spanning Trees, and Dynamic Programming
 Covers greedy algorithms (scheduling, minimum spanning trees, clustering, Huffman codes) and dynamic programming (knapsack, sequence alignment, optimal search trees).
 Part 4: Shortest Paths Revisited, NPComplete Problems and What To Do About Them
 Covers shortest paths (BellmanFord, FloydWarshall, Johnson), NPcompleteness and what it means for the algorithm designer, and strategies for coping with computationally intractable problems (analysis of heuristics, local search).
These courses have appeared on various "top MOOCs of all time" lists, like
here and here.
New sessions begin every few weeks.
MOOCs on EdX
The specialization above subsumes the following older versions:
Stanford lectures on YouTube

20
Video
Lectures on the Design
and Analysis of Algorithms, covering most of the above Coursera MOOCs,
for those of you who prefer blackboard lectures
(from Stanford's CS161, Winter 2011).
 Warning/apology: the audio is suboptimal on a few segements
of these lectures.

20 Video Lectures from A Second Course in Algorithms
(Stanford's CS261, Winter 2016).
Lecture notes are here
 Topics include: algorithms for maximum flow and minimum cuts
(augmenting paths, pushrelabel etc.); bipartite matching and
generalizations; linear programming; duality; online
regretminimization and the multiplicative weights algorithm; online
algorithms; design and analysis of approximation algorithms; the
traveling salesman problem; essential tools for the analysis of
randomized algorithms; beating bruteforce search for NPhard
problems.

20 Video Lectures on Algorithmic Game Theory
(from Stanford's CS364A, Fall 2013). Lecture notes are here
 Topics include: auction and mechanism design (Vickrey and Myerson
auctions, VCG mechanism, etc.); the "price of anarchy" (selfish
routing, smoothness, etc.); learning in games (noregret algorithms,
etc.); complexity of Nash equilibria (PLS and PPADcompleteness).
Case studies include: keyword search auctions, combinatorial auctions for spectrum, kidney exchange, and communication network management.

20 Video Lectures on Advanced Mechanism Design
(from Stanford's CS364B, Winter 2014). Lecture notes are here
 Topics include:
combinatorial auctions; Walrasian equilibria and the gross substitutes
condition;
ascending and ex post implementations; truthful approximation mechanisms;
blackbox reductions; simple auctions and equilibrium guarantees for
them (BayesNash smoothness, etc.);
Border's theorem; multiparameter revenuemaximization.

20 Video Lectures on Beyond WorstCase Analysis
(from Stanford's CS264, Fall 2014). Lecture notes are here
 Topics include: instance optimality;
parameterized analysis and condition numbers;
stable clustering;
models of data
(pseudorandomness, locality, diffuse adversaries, etc.);
distributional models;
smoothed analysis;
planted and semirandom graph models;
exact recovery (compressive sensing, LP decoding).
Motivating problems drawn from online algorithms, machine learning,
computational geometry, graph partitioning, linear programming,
hashing, etc.
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