There are two types of array.

One Dimensional Array

Syntax for default values:

int[] num = new int[5];

Or (less preferred)

int num[] = new int[5];

Syntax with values given (variable/field initialization):

int[] num = {1,2,3,4,5};

Or (less preferred)

int num[] = {1, 2, 3, 4, 5};

Note: For convenience int[] num is preferable because it clearly tells that you are talking here about array. Otherwise no difference. Not at all.

Multidimensional array

Declaration

int[][] num = new int[5][2];

Or

int num[][] = new int[5][2];

Or

int[] num[] = new int[5][2];

Initialization

 num[0][0]=1;
 num[0][1]=2;
 num[1][0]=1;
 num[1][1]=2;
 num[2][0]=1;
 num[2][1]=2;
 num[3][0]=1;
 num[3][1]=2;
 num[4][0]=1;
 num[4][1]=2;

Or

 int[][] num={ {1,2}, {1,2}, {1,2}, {1,2}, {1,2} };

Ragged Array (or Non-rectangular Array)

 int[][] num = new int[5][];
 num[0] = new int[1];
 num[1] = new int[5];
 num[2] = new int[2];
 num[3] = new int[3];

So here we are defining columns explicitly.
Another Way:

int[][] num={ {1}, {1,2}, {1,2,3,4,5}, {1,2}, {1,2,3} };

For Accessing:

for (int i=0; i<(num.length); i++ ) {
    for (int j=0;j<num[i].length;j++)
        System.out.println(num[i][j]);
}

Alternatively:

for (int[] a : num) {
  for (int i : a) {
    System.out.println(i);
  }
}

Ragged arrays are multidimensional arrays.
For explanation see multidimensional array detail at the official java tutorials

Concise update for Java SE 9

Reference arrays are bad. For this case we are after a set. Since Java SE 9 we have Set.of.

private static final Set<String> VALUES = Set.of(
    "AB","BC","CD","AE"
);

"Given String s, is there a good way of testing whether VALUES contains s?"

VALUES.contains(s)

O(1).

The right type, immutable, O(1) and concise. Beautiful.*

Original answer details

Just to clear the code up to start with. We have (corrected):

public static final String[] VALUES = new String[] {"AB","BC","CD","AE"};

This is a mutable static which FindBugs will tell you is very naughty. Do not modify statics and do not allow other code to do so also. At an absolute minimum, the field should be private:

private static final String[] VALUES = new String[] {"AB","BC","CD","AE"};

(Note, you can actually drop the new String[]; bit.)

Reference arrays are still bad and we want a set:

private static final Set<String> VALUES = new HashSet<String>(Arrays.asList(
     new String[] {"AB","BC","CD","AE"}
));

(Paranoid people, such as myself, may feel more at ease if this was wrapped in Collections.unmodifiableSet - it could then even be made public.)

(*To be a little more on brand, the collections API is predictably still missing immutable collection types and the syntax is still far too verbose, for my tastes.)