Title
The title "The Love Song of J.Alfred Prufrock" suggests the idea of a not common love song  and at the same time it reminds to the Medieval songs, expression of a world based on moral principles and values that does not exist anymore. Moreover the attribution of the song to J.Alfred Prufrock makes the reader curios in order to understand why Eliot decided to explicate it.

Form
As the reader goes on he realizes that Eliot uses the dramatic monologue as a form for his poem and that is why he attributes the song to J.Alfred Prufrock.  
The dramatic monologue  is a monologue, realized as a poetic text, in which the poet commits his thoughts and his ideas to a speaking voice ( in this case to Prufrock) called dramatis personae or "maschera". It allowds the poet to take the distances from both the reader and the character. It follows that he has an emotional distance that will lately be known as impersonality of the artist.Last but not least, the dramatic monologue permits the reader to penetrate the most intimate and deepest part of the character who, through what he says and especially through what he doesn't say, reveals, to the intelligent and careful reader, all the things he is trying to hide.

Summary
1-36
J. Alfred Prufrock, a presumably middle-aged, intellectual, indecisive man, invites the reader along with him through the modern city. He describes the street scene and notes a social gathering of women discussing Renaissance artist Michelangelo. He describes yellow smoke and fog outside the house of the gathering, and keeps insisting that there will be time to do many things in the social world.

37-86
Prufrock agonizes over his social actions, worrying over how others will see him. He thinks about women's arms and perfume, but does not know how to act. He walks through the streets and watches lonely men leaning out their windows. The day passes but he cannot muster the strength to act, and he admits that he is afraid.

87-131
Prufrock wonders if, after various social gestures, it would have been worthwhile to act decisively if it resulted in a woman's rejection of him. He thinks he is not a Prince Hamlet figure, but a secondary character in life. Worried over growing old, he adopts the fashions of youth. By the beach, he sees images of mermaids singing and swimming.

Main themes
Paralysis and decadence of values

Analysis
The song starts with a Dante quote taken from the Inferno that has the function to introduce the situation and put in result the dramatic condition of men on earth not so different from the ones in hell.

Prufrock is on earth, in a lonely, alienating city. As a matter of fact the images of the city are sterile and deathly:  the night sky looks "Like a patient etherized upon a table" (3), while down below barren "half-deserted streets" (4) reveal "one-night cheap hotels / And sawdust restaurants" (6-7). The use of enjambment,  further conveys the idea of a labyrinthic city. It follows that the images are undeniably bleak and empty. As the poem goes on Prufrock's imagery progresses from a general look at the skyline to a more specific look to streets,  hotel rooms and sawdust-covered floors in restaurants. This debasement continues throughout the poem, both literally in the verticality of the images and figuratively in their emotional associations for Prufrock.
Indeed, emotional associations are key, since Eliot deploys the objective correlative technique throughout the poem. The above images all speak to some part of Prufrock's personality. The etherized patient, for instance, reflects his paralysis (his inability to act) while the images of the city depict a certain lost loneliness. The objective correlative switches to the "yellow fog that rubs its back upon the windowpanes" (14) in the second stanza described as a feline. The fog/cat seems to be looking in on the roomful of fashionable women "talking of Michelangelo" (13). Unable to enter, it lingers pathetically on the outside of the house, and we can imagine Prufrock avoiding, yet desiring, physical contact in much the same way.
 
From the text emerges  another technique Eliot and the Modernists used: fragmentation.
Images and allusions are not the only fragmented features of "Prufrock." The rhythm of the lines is deliberately irregular. At times in unrhymed free verse, Eliot occasionally rhymes for long stretches (lines 4-12) and then not at all; his rhyme scheme itself seems like the confusing "Streets that follow like a tedious argument" (8). He also twice uses the refrain of "In the room the women come and go / Talking of Michelangelo" (13-14, 35-36), and often begins lines with the word "And" (7, 23, 29 32, 33). As the word found in three of these lines implies - "time" (23, 29, 32) - the repetitions have something to do with Prufrock's relationship with time.
Prufrock  seems rooted in the present tense as the lines "And time yet for a hundred indecisions, / And for a hundred visions and revisions, / Before the taking of a toast and tea" (32-34) suggest. The opening image of the evening "spread out" (2) against the sky reminds to the concept of time of the French philosopher Bergson. He argues that time is a single, continuous, and flowing "durée," or duration, in which past cannot be isolated from present and future rather than a succession of discrete steps with distinct tenses. However Prufrock seems to be stucked in the present, uncapable to make decision: he is parlyzed.

Prufrock's anxiety is rooted in the social world. Not only is he afraid to confront the woman talking of Michelangelo, he also seems intimidated by the social posturing he must engage in:
There will be time, there will be time
To prepare a face to meet the faces that you meet;
There will be time to murder and create,
And time for all the works and days of hands
That lift and drop a question on your plate;

From these lines the intelligent reader can understand that Prufrock, as he will reveal later in the song, is "afraid", so he keeps procrastinating assuming that "there will be time". As a result, the reader is a further confirm of Prufrock's inability to act.
Prufrock's social paralysis is diagnosed in these six stanzas.  He continues asking himself questions about how to comport himself, but admits he will reverse these decisions soon. His inaction is constantly tied to the social world: "Should I, after tea and cakes and ices, / Have the strength to force the moment to its crisis?" (79-80) The somewhat silly rhyme here underscores the absurdity of Prufrock's concerns.
Anxiety is foremost a concern with the future, and Prufrock continues to show his inability to advance in time. Of the six stanzas here, four begin with "And" (37, 55, 62, 75) while five lines at the end of different stanzas do (61, 68-69, 85-86), suggesting a repetitive, inescapable present tense. In addition, Prufrock's refrain "And indeed there will be time" (23, 37) is very significant. Rather than hurrying his lady, Prufrock makes excuses for himself; he assures himself there will be time to act, although his repetitive, paralytic nature has so far belied that.
Not only is Prufrock paralyzed in the present, but he seems to have a disordered sense of time. He describes the "evenings, mornings, afternoons" (50), and the odd order gives us pause. While it primarily describes a cycle from night to the next day, reinforcing the idea of repetition, its abrupt switch from "evenings" to "mornings" echoes Eliot's imagesin the first three stanzas.
 The final section of the poem swings from fairly concrete, realistic scenes from the social world - "After the cups, the marmalade, the teaŠAfter the novels, and the teacups, after the skirts that trail along the floor" (88, 102) - to fantastic images of mermaids "riding seaward on the waves / Combing the white hair of the waves blown back" (126-127).Prufrock  seems to be  unsure: "It is impossible to say just what I mean! / But as if a magic lantern threw the nerves in patterns on a screen" (104-105).
But Prufrock shows a wise self-regard when he admits he is
not Prince Hamlet, nor was meant to be;
Am an attendant lord, one that will do
To swell a progress, start a scene or two,
Advise the prince; no doubt, an easy tool,
Deferential, glad to be of use,
Politic, cautious, and meticulous;

The allusion, then, is somewhat ironic, since Prufrock is not even as decisive as Hamlet is. The only thing in Prufrock's life not paralyzed is time; it marches on, and Prufrock laments "I grow old . . . I grow old . . . / I shall wear the bottoms of my trousers rolled" (121). While he continues to be anxious about the future, Prufrock now seems to regard the future, paradoxically, from a future standpoint. His refrain of "And would it have been worth it, after all" (87, 99) places his actions in the perfect conditional tense. It is as though he is reviewing actions he has yet to take. Either time has accelerated his aging process, or this look to the past is a way for Prufrock to delude himself into thinking he has made some decisive progress in life.
Prufrock, knows he is going to die soon but he still cannot even "dare to eat a peach" (122). that puts in resul Prufrock's anxiety.
Prufrock has just wondered "Shall I part my hair behind?" (122), and previously he has agonized over his bald spot, turned his keen eye to the women's arms "downed with light brown hair!" (64), and agonized over eating a fuzzy peach. Mermaids are conventionally depicted combing their hair with a mirror, so as symbols of vanity and lush beauty - "wreathed with seaweed red and brown" (130), they possess even more artificial hair - they threaten Prufrock (whose thinning hair is perhaps now a salt-and-pepper mixture of "white and black" and no longer "red and brown").
When Prufrock finishes the poem by pronouncing "We have lingered in the chambers of the seaŠTill human voices wake us, and we drown" (129, 131), he completes the vertical descent Eliot has been deploying throughout the poem. He has plunged into his own Dantesque underworld and, through the "We" pronoun, forces us to accompany him - hoping, like da Montefeltro from the epigraph, that we will not be able to return to the mermaids on top and shame him by repeating his story.
The concluding two three-line stanzas act as a sestet (six lines).  Prufrock, does not even have an unattainable ideal love. He has unattainable, frustrated, paralyzed desire for all women who reject him; they are all inaccessible, and any reminder of the social world ("human voices") drowns him - and, he hopes, his reader-as-Dante - deeper in his watery Hell.