what are main similarities and differences between rural life and court life in the play as you like it?
One of the primary themes in "As You Like It" is the contrast between life at court and life in the Forest of Arden, and the two settings are so different that, while it is relatively easy to illustrate their differences, the likeliness are essentially non-existent. Shakespeare used the two settings to describe the fundamental differences between court life, which is political and corrupt, and life in the forest, which can be uncomfortable, but is free from politics, corruption, and intrigue.
For example, as Charles describes Duke Senior's situation at the beginning of the play, he say the Duke and his supporters have been banished to
the Forest of Arden, and/many/merry men with him; and there they live like the old/Robin Hood/of England.
Aside from the fact that Duke Senior is now at "out-law," which, in terms of English common law means that he no longer has the benefit of the law's protection, clearly Shakespeare describes the Forest of Arden as a much better place, linking it to one of most important cultural heroes of medieval England, Robin Hood and his merry men. It is not coincidental that Shakespeare describes Duke Senior's followers as "merry men."
Charles goes on to link the Forest of Arden with Paradise:
They say many young gentlemen flock to him every/day, and fleet the time carelessly, as they did in the golden world.
The reference to "golden world" is to a time and place in Greek mythology when peace ruled men in basically an earthly paradise.
The forest, however, has some drawbacks--one might not die from political corruptness and an evil ruler in the court, but life in Arden can be difficult:
And churlish chiding of the winter's wind,/Which when it bites and blows upon my body,/Even till I shrink with cold. . . .
The drawbacks of living in Nature are physical, and though they cause discomfort, Duke Senior concludes that "these are counsellors/That feelingly persuade me what I am." In other words, the forces of nature that cause his discomfort simply remind him that he's a man living in Nature. The wind is a "counsellor" that he can trust--as opposed, for example, the counsellors in court who may lie to him.
The importance contrast between life in Arden and life at court is perfectly summed up by Duke Senior when he says:
Are not these woods/More free from peril than the envious court?
Again, he acknowledges the real problem of physical discomfort in Arden, but when he compares the evils waiting for him at court, the relatively minor inconvenience of cold weather pales in comparison with the ultimate inconvenience of getting killed or thrown into jail permanently if he returns to court.