The phrase 'The Science of Happiness' seems something of an oxymoron since science is objective and happiness is subjective. However following on with the edX online course Dacher Kellner, one of the instructors, took a brief tour of how some of the great thinkers grappled with the fundamental question: what is happiness? --- from Confucius, Lao Tzu, Buddhism, the Greek philosophers, hedonism to the 19th century utilitarianism of John Stuart Mill (the greatest happiness for the greatest number of people).
And now we have the scientific view (not entirely formed yet) which uses functional MRI (fMRI) and measurements of neurotransmitters and hormones like serotonin, dopamine, oxytocin, endorphins, etc. It seems that the brain sits in a chemical bath of these substances which modulate its synaptic activity.
In one real but satirical fMRI study, a dead salmon was shown pictures of humans in different emotional states. The authors provided evidence, according to two different commonly-used statistical tests, of areas in the salmon's brain suggesting meaningful activity!!