Selection sort implementation in Java
I suggest you format

for(int i = 0; i &lt; arrayToSort.size(); i++) {   // i = leftmost index of unsorted part of the array


as

// i = leftmost index of unsorted part of the array
for(int i = 0; i &lt; arrayToSort.size(); i++) {


swap takes arguments a, b and arrayToSort. These arguments could be more explanatory: swap doesn't sort anything and it doesn't take an array, and a and b don't say much.

It's canonical to use i and j as indices, so that would be more appropriate - although longer names wouldn't hurt either. The List argument would be better as items or similar. items is this-like, so put it first.

private static void swap(List&lt;Integer&gt; items, int i, int j) {
    int temp = items.get(i);
    items.set(i, items.get(j));
    items.set(j, temp);
}


You can also make this more like the OpenJDK implementation by using the return value from set:

private static void swap(List&lt;Integer&gt; items, int i, int j) {
    int temp = items.set(i, items.get(j));
    items.set(j, temp);
}


or even

private static void swap(List&lt;Integer&gt; items, int i, int j) {
    items.set(j, items.set(i, items.get(j)));
}


You could also make it generic.

private static &lt;T&gt; void swap(List&lt;T&gt; items, int i, int j) {
    items.set(j, items.set(i, items.get(j)));
}


Your sort is of course inefficient; you're using selection sort. However, you can at least make it a little faster. First neaten it up - including changing the name to something more descriptive. Note that minimumValue is not a value but an index - this should be fixed.

public static void sortInPlace(List&lt;Integer&gt; toSort){
    // i = leftmost index of unsorted part of the array
    for(int i = 0; i &lt; toSort.size(); i++) {
        int minimumValue = i;
        for(int j = i; j &lt; toSort.size(); j++) {
            if(toSort.get(j) &lt; toSort.get(minimumValue)) {
                minimumValue = j;
            }
        }
        swap(toSort, i, minimumValue);
    }
}


You can change the inner loop to start at i + 1. You can also cache the value to halve the number of toSort.gets you make.

public static void sortInPlace(List&lt;Integer&gt; toSort){
    // i = leftmost index of unsorted part of the array
    for(int i = 0; i &lt; toSort.size(); i++) {
        int minimumIndex = i;
        int minimumValue = toSort.get(i);
        for(int j = i + 1; j &lt; toSort.size(); j++) {
            if(toSort.get(j) &lt; minimumValue) {
                minimumIndex = j;
                minimumValue = toSort.get(j);
            }
        }

        swap(toSort, i, minimumIndex);
    }
}


This gives a noticeable speed improvement.

Frankly, though, if you want a reasonably fast integer selection sort, use an array. int[] is unboxed, which means that it's some 4x the speed. It's actually faster to copy into a temporary int[], sort and copy it back than to sort in a boxed List.