“Love Poem for a Wife, 1” by A. K. Ramanujan provides plenty of material for a detailed analysis. You should look at the poem's structure, its content and themes, and the language the poet uses to enhance his ideas.
Let's begin with the poem's structure. Ramanujan divides his poem into twelve stanzas. Most of them have seven lines, although stanza 4 has eight lines and stanzas 5 and 12 have six lines. The poet uses free verse with no consistent rhythm or rhyme. His poetry reads very much like prose, and his lines are highly enjambed, meaning that sentences flow freely from one line to the next without pauses at the end of the lines.
While from the title we might expect a poem about how much the poet loves his wife, Ramanujan actually focuses his attention on how he and his wife still have much to learn about each other, especially about their early lives with their families. They each hear plenty of stories about their youth, but they cannot relive those days nor experience each other's memories to the fullest. The poet's wife, for instance, never met his father, who has been dead for many years. The poet cannot know what his wife's father was like when she was a child, for the years have “mellowed” him. The family stories and pictures help, but they are not enough. The poet often feels left out when his wife is with her family, arguing with her brother about the disputed location of a bathroom. The poet and his sister-in-law stand to one side as the siblings draw blueprints and make wagers. They cannot participate, and the poet feels disconnected. Indeed, disconnection is one of the major themes of the poem. The poet feels as though he and his wife are somehow disconnected because of their separate histories, and he does not know how to overcome the separations except by the facetious “suggestions” he makes at the end of the poem.
Finally, you should look closely at the poet's use of language and imagery. The phrase “unshared childhood” in the first stanza sets up the poem's theme nicely while offering a bit of a jolt by its unexpectedness (people usually speak of shared experiences rather than “unshared” experiences). The poet uses a metaphor in the third stanza when he talks about how he passes “from ghost to real / and back again” in family stories. His wife catches a glimpse of something solid that quickly fades. The poet provides tantalizing images of his father's noisy bathing and his parents' wedding photo. He also refers to himself and his sister-in-law as “blank cut-outs” who must merely stand to one side as his wife and her brother argue. You might also consider the use of anecdotes in the poem, for the poet includes several of them, and they mirror his claims that he cannot fully know his wife's history.