A hash table is a data structure that can implement a function whose domain is a finite set. An element of the domain is called a key. The hash table stores the keyvalue pairs in such a way that when presented with a key, the corresponding value can be quickly recovered.
A dictionary could be implemented as a hash table: the keys would be the words in the language, and the values could be the definitions of the words.
A phone book could also be implemented as a hash table: the keys would be the names of the subscribers, and the values could be the corresponding phone numbers. (We exclude the possibility of two subscribers with the same name.)
As an example we implement a phone book.
i1 : book = new HashTable from {
"Joe" => "3445567",
"Sarah" => "5674223",
"John" => "3221456"}
o1 = HashTable{"Joe" => 3445567 }
"John" => 3221456
"Sarah" => 5674223
o1 : HashTable

We use the operator
# to obtain values from the phone book.
i2 : book#"Sarah"
o2 = 5674223

The operator
#? can be used to tell us whether a given key has an entry in the hash table.
i3 : book#?"Mary"
o3 = false

We have implemented the notion of set via hash tables in which every value is the number 1.
i4 : x = set {a,b,c,r,t}
o4 = set {a, b, c, r, t}
o4 : Set

i5 : peek x
o5 = Set{a => 1}
b => 1
c => 1
r => 1
t => 1

i6 : x#?a
o6 = true

i7 : x#?4
o7 = false

There is a type of hash table that is mutable, i.e., a hash table whose entries can be changed. They are changed with assignment statements of the form
x#key=value.
i8 : x = new MutableHashTable;

i9 : x#"Joe" = "3445567";

i10 : x#3 = {a,b,c};

i11 : x#{1,2} = 44;

i12 : x#3
o12 = {a, b, c}
o12 : List

i13 : x#?4
o13 = false

When a mutable hash table is printed, its contents are not displayed. This prevents infinite loops in printing routines.
i14 : x
o14 = MutableHashTable{...3...}
o14 : MutableHashTable

Use
peek to see the contents of a mutable hash table.
i15 : peek x
o15 = MutableHashTable{{1, 2} => 44 }
3 => {a, b, c}
Joe => 3445567

A variant of
# is
.. It takes only global symbols as keys, and ignores their values.
i16 : p=4;

i17 : x.p = 444;

i18 : x.p
o18 = 444

i19 : x#?4
o19 = false
