I have list of Joda-Time Interval objects.
List<Interval> intervals = new ArrayList<Interval>();
How can I sort the intervals on the beginning Date of each interval. The intervals are not overlapping
Just create a Comparator<Interval> which compares by start times:
public class IntervalStartComparator implements Comparator<Interval> {
    @Override
    public int compare(Interval x, Interval y) {
        return x.getStart().compareTo(y.getStart());
    }
}
Then sort using that:
Collections.sort(intervals, new IntervalStartComparator());
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