Questions about the science and art of determining properties of algorithms, often including correctness, runtime and space usage. Use the [runtime-analysis] tag for questions about the runtime of algorithms.
This question is for all aspects of analysis of algorithms, including their correctness, their running time, their space usage, or other properties.
If you are asking specifically about the running time of an algorithm, runtime-analysis might be more appropriate.
We have several reference questions that provide useful material about the analysis of algorithms:
See How to come up with the runtime of algorithms? for a broad overview of the techniques used in runtime analysis, and Is there a system behind the magic of algorithm analysis? for a more systematic treatment of how to take an algorithm and mathematically model its running time.
See How do O and Ω relate to worst and best case? and How does one know which notation of time complexity analysis to use? for mathematical background on asymptotic analysis and notations.
See How do I write a proof using induction on the length of the input string? for how to use proof by induction to prove the correctness of some kinds of algorithms.
Many elementary questions about algorithm analysis can be solved using the techniques in those reference questions, so you are encouraged to check whether your problem can be solved using those standard techniques before asking.