One core teaching of classic Buddhism is “the Brahma Viharas” (the “divine abodes”, aka “the four illimitables”). The Brahma Viharas are one of the many lists of virtues that one is to cultivate in the classic Buddhist path, but they are virtues that are specifically for cultivation in the heart.
The first on the list is a well known Buddhist virtue : “metta” (“maitri” in Sanskrit), which translates as loving-kindness. I understand this as a warm hearted feeling of wishing others well being at all times. The “far enemy” (the polar opposite) of metta is said to be hate, and its “near enemy” (in other words, what it can easily be mistaken for but is essentially not) is said to be simple garden-variety preference-laced affection.
The second attribute is “karuna”, compassion, which I understand to be a warm hearted feeling of wishing others well being specifically when they are not doing so well. The far enemy of karuna is contempt, and its near enemy is pity.
The third Brahma Vihara is “mudita”, sympathetic joy, which I understand as a warm-hearted feeling of wishing others well being when they are doing great. The far enemy of mudita is jealousy, and its near enemy is joy at other’s unhealthy success (for example, your friend’s joy when their rival just has to declare bankrupcy).
The final brahma vihara, the one I believe balances out the other three and stops them from being too gushy, is “upekka”, equanimity, an evenness of emotionality whatever happens. The far enemy of upekka is resentment, and its near enemy is indifference.
The four residence halls at the Spirit Rock meditation center in Marin are named Metta, Karuna, Mudita, and Upekka.
Some people may be surprised by the “Upekka Prayer” – it probably doesn’t match many people’s conception of what Buddhism is all about (which is more like lovingkindness, compassion, and sympathetic joy). You could say that the Upekka prayer is a verse for Buddhists to chant when they get too codependent, too wrapped up in another person’s guff, and when their Metta, Karuna, and Mudita gets all gooey and attached. The verse is as follows:
You are the owner and heir to your own karma. Your outcomes depend on your choices and actions and not my good wishes. No matter how I might wish things to be well for you, things are as they actually are. Although I wish only the best for you, I also know that your happiness and unhappiness depends upon your actions, not my wishes for you. Whether you understand it or not, things are unfolding for you according to a lawful nature.
[edit: When I was in India, I visited a Tibetan Buddhist teaching center, and registered to attend one of their intermediate courses. They told me that, to take any of their courses, I had to start with their introduction to Tibetan Buddhist philosophy course, just to make sure that I was on the same page with their teachings. So, I took the introductory course. While I met many wonderful people during those ten days, it occurred to me afterwards that I was already familiar with every single piece of Dharma that the teachers presented – every single one, except that I learned Tibetan Buddhists evidently understand “upekka” in the Brahma Viharas to signify less having a certain detached coolness in dealing with folks, and more as treating all people and beings with an impartial equal warmth, without playing favorites.]