Depending on season of the harvest, green tea leaves contain 1.6 - 3.5% caffeine. What does it mean? Let's say 2.5 grams of tea leaves are in a teabag and steep the teabag in 8 oz. hot water. In the 2.5 grams of tea leaves, there is 40 - 88 milligrams of caffeine, but not all of them are extracted into the water. In the first 90 seconds, less than 50% of the caffeine come out, so in the 8 oz. water, there is only 20 - 44 milligrams of caffeine. (In the FDA website, I found 100 - 200 milligrams of caffeine is moderate and not farmful.) Additionally, green tea has theanine which is unique amino acid almost exclusively found in green tea. Theanine counteracts to caffeine and reduce the caffeine's alerting influence.
Caffeine is not always bad guy. Do you know what caffeine does for you? Caffine accelerates metabolism and helps you to loose weight. Many people say "green tea help to loose weight," and caffeine is highly related to this benefit. Caffeine also has awakening effect which sometime bother you in night time but usually help you to focus on your work or study. Some studies in Japan say combination of caffeine and theanine bring you the ideal relaxation. Caffeine counteracts to drowsiness, and theanine reduces mental stress.
Everything, even water, can be harmful if you take too much. Moderate amount of caffeine will help you to be healthy. Many Japanese drink a cup of green tea after every meal, and this is the reason they live longer.