Sort an Integer List

05AB1E, 2 bytes

Code:

ϧ

Same algorithm as the Jelly answer. Computes all permutations of the input and pops out the smallest one.

Try it online!

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A more efficient method is:

E[ß,Ž

Performs selection sort. Uses CP-1252 encoding.

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Jelly, 3 bytes

Œ!Ṃ

This generates all permutations of the input list, then selects the lexographically smallest permutation. Very efficient.

Credits to @Adnan who had the same idea independently.

Try it online!

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Jelly, 4 bytes

ṂrṀf

This builds the range from the minimum of the list to the maximum of the list, then discards the range elements not present in the original list. This is technically a bucket sort, with very small buckets. I'm not aware of a name for this specific variant.

Try it online!

How it works

ṂrṀf  Main link. Argument: A (list/comma-separated string)

Ṃ     Compute the minimum of A.
  Ṁ   Compute the maximum of A.
 r    Yield the inclusive range from the minimum to the maximum.
   f  Filter the range by presence in A.

Python, 46 45 bytes

lambda l:[l.pop(l.index(min(l)))for _ in 1*l]

Simple selection sort.