Buddha Abhidhamma - Ultimate Science - BuddhaNet

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In practising loving-kindness, we meditate: “May all be
happy.” In cultivating compassion, we meditate: “May all be
free from miseries.” For exercising mudità, we rejoice on the
prosperity of beings and meditate: “May their gain be with them
for a long time”. In practising upekkhà, we maintain a balanced
mind and meditate: “All beings are as they are conditioned by
their kamma”.
Anyone who is pervading the whole world with lovingkindness,
compassion, sympathetic joy or equanimity is said to
be living in the ‘sublime abode’ or ‘brahma abode’. So the four
illimitables are also known as brahma-vihàra, i.e., sublime modes
of living.
Mettà is the sincere wish for the good and welfare of all. It
discards illwill which is its direct enemy. Its indirect enemy is
affection (pema). Benevolent attitude is its chief characteristic.
Karunà makes the hearts of the good quiver when others
are afflicted with sorrow. The wish to remove the sufferings of
others is its chief characteristic. It discards cruelty or wickedness
(hiõsa) which is its direct enemy. Its indirect enemy is grief
(domanassa).
Mudità is not mere sympathy but appreciative joy. Its chief
characteristic is to rejoice in others’ prosperity. Its direct enemy
is jealousy (issà) and its indirect enemy is exultation (pahàsa). It
discards dislike (harati).
Upekkhà views living beings impartially, i.e., neither with
attachment nor with aversion. It is the balanced state of mind.
Its direct enemy is passion (ràga), and its indirect enemy is
unintelligent indifference. Impartial attitude is its chief
characteristic.