The most obvious is the director's obsession with American cinema. That his films are mere tributes to American cinema, or stern deconstructions of them. It is true that Jef Costello wears the classic film noir garb of mac and derby, but so do at least 400 men in Paris. And it is true that Melville rigorously exposes the myth of the gangster, but, most importantly, of masculinity and its power.
Elaborate theories of psychoanalysis are usually brought in here, the idea that Jef begins the film 'whole', looking at the mirror; during the course of the narrative he loses this self-sufficient image, cracking up as it fragments, split by mirrors, trapped behind bars (although the halved banknotes he consciously plays with at the beginning might qualify this).
Others comment on the film less as a gangster film than a dramatisation of particular philosophies. Some see Jef as an example of existentialist man, a man who does not exist except through his acts - the film patiently records endless scenes of Jef walking, staring, preparing for his jobs etc. His final ritual is a preparation for his death; as existentialism suggests, friends, social purpose etc. fall away, and one is left alone with one's fate.
Or as an expression of fatalistic Orientalist ethics (the film IS called 'Le Samourai') concerning solitude and the inevitability of death. Melville himself offered two possible interpretations - as a study in schizophrenia, and as an allegory of Man (Jef) pursued by Destiny (the Inspector) into the arms of Death (Valerie, the pianist).
All of these, of course, are valid interpretations. I am more sympathetic to those who see 'Samourai' as a dream, a study in solitude, or a portrait of mental breakdown. The film's action takes place largely at night; there is a frequently oneiric tone to Melville's style, the endless walking, the silence, the deliberate paring down of the mise-en-scene to near-monochrome. Jef's impassivity is comparable to that of a somnambulist, walking mechanically down countless corridors. As in a dream, whole sequences are repeated in exactly the same way. We keep returning to the same few locales. The film opens with Jef lying smoking in bed, in the dark; one powerful scene is Jef waking up after he has bandaged his wounded arm - has he had a nightmare, or is it the sound of a passing truck?
'Samourai' is also much more moving as a story of solitude than Antonioni's entire oeuvre put together. The only sure thing in this strange and enigmatic film is Jef's loneliness, living with his only friend, a caged bullfinch (usually a symbol of female entrapment) in a dismally run-down, sparse grey bedsit, prey to any intruders. Although he is constantly forced into the centre of the city by work and the police, he is safer on the margins, in anonymous streets, abandoned railway yards, disused buildings. Or at least he was before all the trouble started.
He is defined against the grim, geometric anonymity of modern life, his milieu as soulless and constricting as the plot he moves in, the elevator shafts that imprison him. He is the image of man in a surveillance society, an innocent man (until proven guilty) having his every move followed by a police happy to use morality as a threat (many people see Melville's films as sublimated allegories of France under the Occupation).
His only contact with people is in the preparation of death; his is a sterile, self-negating existence, ascetic as a monk (his uniform as ritual vestments). That Jef is a tragically lonely man is undoubted. There are two heartbreaking moments in this cool, austere film, when emotion breaks Alain Delon's astonishing performance, the most beautiful man in the movies letting slip just like the stills moving in 'La Jetee': when he goes back to the scene of the crime and looks at the pianist; his face for a brief second seems absolutely distraught, helpless, a child looking for a mother to reassure him (this is the key to the film, I believe, Jef the lonely wanderer searching for home); the second, after the celebrated Metro chase, in the stolen car, his face, for a moment, betraying hear-beating terror. At these moments, allegories and theories simply break down.
Jef's mental breakdown is, of course, linked to all this. Over the credits, Jef smokes alone in his bedroom, barely visible - the two bright windows look like eyes, as in Beckett's 'End Game', a figure for the mind, a mind at the end of its tether as seen by Melville's horizontal use of Hitchcock's famous 'Vertigo' shot, contracting and constricting the room to breaking point, revealing the instability of this 'safe' haven, and Jef's image of himself.
Mental deterioration is usually a subject of horror movies - the score features frequent bursts of chilling organ; when Jef goes to collect his car and gun for the contract, his accomplice, lit by a lamp, looks like a terrifying spirit. Jef is a trapped character, in his room, identity, plot; by the police and the gangsters; by geography, shadows, corridors; by the loop of time that forces him to return again and again to the same point - he is in hell; the only way out is self extinction.
It is important not to see Melville as child of Sartre, which limits him, but of Nabokov, whose complex procedures of ludic expression find a cinematic equivalent in his work - it is vitally important not to take him at face value. Jef's shooting of Rey - impossible, magical - is pure Nabokov.
I could go on - the Benjaminian idea of the flaneur and Paris; the extraordinary, near-futuristic sets; the comedy (e.g. see who Jef rides with in the police van answering to the same description); its remarkable analysis of the gaze; the brilliance of its action and suspense mechanics; the running motif of the theatre, performing, acting (in both senses) - Jef's costume; the line-up in a theatre-like space; the closing 'show is over' drum-roll.
Everything about this film, as John Woo noted, is perfect, but there is one sequence, breaking with Melville's calm, distant style throughout, that I would list on my ten best ever - as Jef goes to collect the cash and is instead faced with a gun - firstly he faces the audience; we could be no closer. Then, just as the struggle begins, Melville cuts away, his camera manically panning away from the action behind bridge grills, following Jef as he runs and ineffectually chases his assailant's car. It is a heartstopping moment in a film still too little known. I've just watched it twice in two days; I really must watch it again.