Rudyard Kipling's Kim is a novel about a young man caught between two cultures, Indian and British. Although of Irish ancestry, Kim has been raised in India. Being Irish in the nineteenth century was a somewhat fraught identity, given that Ireland, like India, had been conquered by England and many Irish were agitating for independence. In India, Kim is brought up by a half-caste, who is also an outsider, and later attaches himself to a Tibetan. All of these positions are marginal ones, which position Kim as located on the fringes of society, looking in from the margins. This position is precisely what makes him such a potentially good spy.
Thus issues of identity are very much at the center of the novel and should be discussed in any interpretation of it. The most important literary theory you should use in discussing the novel is postcolonial criticism, as it addresses this issue of identity in nations which have been colonized by foreign powers.