I wanted to have a chronological order for all the topics for the preparation of IOI and that is why I am creating this thread. The main motive is that my school has allowed me and other interested students to form a group to start preparing students for OIs. I will be introducing it to the junior classes. So, it would be nice if the order started from the very basics and went to intermediate or even advanced if people are willing to contribute. This is a community wiki so feel free to edit it for the help of myself and all those who prepare for IOI in present or future.

But non of these are "chronologically ordered". Topics are better ordered with increasing order of difficulty, starting from changing from Turbo C++ to GNU C++11.

For now, I am creating a very rough order. I hope more people contribute to it. Also, I will keep editing it till I can.

Big O Notation

Ad hoc problems

Brute force

Using DFS

Using BFS

Permutation generation

Subset generation

Maths

[Bit-Manipulation][1]

[Hash-Tables][2]

Greedy

Data structures(Excluding graph)

Arrays

Strings

Vectors

Stack

Queue

Heap

List

Deque

Divide and conquer

Binary search(In an array/On answer)

Merge sort

Segment tree

Merge sort tree

Centroid decomposition

Dynamic Programming

Introduction(Possibly using the classic fibonacci example)

Hey @ista2000 It is really good that you have started it. You can take help from forums too. They include quite good topics. Moreover talking about number theory you can add topics like

1.Euler totient function.
2.Matrix Exponentiation(Not sure whether it's a part of number theory but it is quite useful when you work on recursive function).
3.Fermat Little Theorem is also very important sometimes (in modulo functions)
4.Lastly I remember a topic SOS Dynamic Programming approach. If you want to add. :)

@ista2000 if it is possible then please provide us with links to these topics as there is much information on web and finding a better resource may not be possible for noobs like me so please help by adding links. Anyways nice initiative.