What is the difference between HashSet, LinkedHashSet, and TreeSet?

All three implement Set (no duplicates), backed by different underlying structures:

• HashSet: backed by a HashMap internally (elements stored as keys). O(1) average add/contains/remove, but iteration order is unspecified and can change across JVM versions or even between runs.
• LinkedHashSet: extends HashSet but additionally threads a doubly-linked list through all entries to remember insertion order — iteration order matches the order elements were added, at a modest extra memory cost (the links) and similar O(1) operation cost.
• TreeSet: implements NavigableSet, backed by a red-black tree (TreeMap internally). Elements are always kept in sorted order (natural ordering via Comparable, or a custom Comparator passed to the constructor). Operations are O(log n), and it supports range views (headSet, tailSet, subSet) and nearest-neighbor queries (floor, ceiling, higher, lower).

Set<String> hash = new HashSet<>();       // arbitrary iteration order
Set<String> linked = new LinkedHashSet<>(); // insertion order
Set<String> tree = new TreeSet<>();       // sorted order

Choosing: use HashSet by default for pure membership testing; LinkedHashSet when you need predictable, insertion-ordered iteration without paying for sorting; TreeSet when you need the elements sorted or need range/nearest queries, accepting the O(log n) cost and the requirement that elements be mutually comparable.