Though named after the band's magnum opus, roughly the first half of the book is devoted to tracking Jeff's progress from childhood through touring On Avery Island, and the friends he made along the way that would shape the classic 1998 album. It makes for quite an interesting story, and gives you a good understanding of where the album came from, without tarnishing its mystique.

Cooper lets those involved tell the story, with revealing quotes from nearly everyone directly involved. While Jeff himself declined to be interviewed for the book, he gave his approval, and is present in the form of old interview excerpts and stories remembered by friends. I think this turned out to be a blessing in disguise, as Jeff's detachment is a main element of the story, and if he were sitting there answering questions about the album, it'd likely lessen the impact.

Kim Cooper has made a webpage for the book at http://www.scrammagazine.com/nmh.html

Jeff Mangum. Born in Ruston, Louisiana, Jeff is the man behind the songs of Neutral Milk Hotel. He has also made guest appearances on several records made by his friends (see The Musical Adventures of Jeff Mangum). In addition to music, Jeff is interested in other creative avenues, such as drawing and collage. He currently enjoys a life away from the limelight in New York.
Fun fact: "Jeff" is short for Jefferson.

Julian Koster. Wildcard utility player whose versatility and enthusiasm helped give texture to Neutral Milk Hotel's music by adding singing saw, banjo, accordion, and more. He's also worked with Olivia Tremor Control. Before joining up with Jeff Mangum, Julian had a band called Chocolate USA which put out a couple records in the early 90s. He also releases music with friends under the name The Music Tapes.
Fun fact: Julian used to sell pretzels in Union Square Park, NYC.

Scott Spillane. Known for his stellar work playing horns for Neutral Milk Hotel (trumpet, trombone, flugelhorn), as well as sometimes second guitar, tambourine or whatnot, Scott has also appeared on albums and in live shows by Elephant 6 artists such as Olivia Tremor Control, Of Montreal, and Elf Power. Scott fronts a band called The Gerbils.
Fun fact: Scott and his wife Sally currently reside in Athens, Georgia.

Jeremy Barnes. In addition to being the dynamo drummer for Neutral Milk Hotel, Jeremy has also played as a member of the avant-jazz trio Bablicon, as well as done guest work with the likes of Broadcast, Bright Eyes, Now It's Overhead, and Of Montreal. He currently releases music self-described as "folk-Dada" under the name A Hawk And A Hacksaw.
Fun fact: Jeremy's middle name is Hartford.

Notable "5th Member" types to mention include Robert Schneider and Laura Carter. Robert played here and there on the albums, but not live with the band, due in part to his involvement with his own band, the Apples In Stereo, taking precedence. Laura is a member of the band Elf Power, but she appeared on Aeroplane, and often joined NMH on stage (zanzithophone, keyboard). Other people who would sometimes be part of live performances include Will Westbrook and John D'Azzo, both also members of the Gerbils. Robbie Cucchiaro, who played with Julian in the Music Tapes, also played live with NMH at times. When the bill was shared with other e6 bands, such as Elf Power and Olivia Tremor Control, it was common for members from the bands to join each other on stage.

In addition to that message, Jeff granted an interview to Pitchfork in February 2002 (link). Those seem to be his most recent public comments.
Another in-depth article appeared in the September 4, 2003 issue of Creative Loafing, an Atlanta weekly. That one didn't have direct involvement from Jeff (other than asking the author to leave him alone), but there are quotes from some of Jeff's friends that are somewhat enlightening (link).

Jeff is said to currently be living happily in New York with his wife, filmmaker Astra Taylor. Recent public appearances include briefly guesting at NY shows by his friends Olivia Tremor Control (August 2005) and Elf Power (November 2005). He also joined the E6 "Holiday Surprise tour" in October 2008, performing the NMH non-album song "Engine" with Julian on several of the tour's stops (Scott and Jeremy were both on the tour as well, but a full-band reunion never transpired).

Jeff also emerges with charitable pieces from time to time, such as drawings and autographed NMH albums, usually sold or auctioned on his behalf by friends or organizations supporting humanitarian causes, including Children of the Blue Sky.

Friends say he still writes and records songs, but isn't interested in releasing them at the moment.

There are currently plans to release a two-volume set of early Neutral Milk Hotel, featuring music from the early, self-released cassettes, live performances, and unreleased recordings. The band wants to do this as a result of the excessive prices at which bootlegs are currently selling online and elsewhere. They will be available from Orange Twin. No date has been decided upon for released. It could be awhile in the future.

Jeff has been working on a collection of short stories. He also just joined the circus and wants to make a movie about snails.

In the several years that passed since that was posted, there's been no news regarding Jeff's stories or movies.
And for a long time there was no news about the proposed rarities album. Then in March 2004, hope sparked anew, with the Orange Twin record label's own Laura Carter posting the following on a message board:

we've gotten half an album's worth of non released NMH/Jeff songs approved by Jeff, but the rest he's not interested in releasing, so we are trying to get more stuff that he likes. We are thinking now that it will be two discs, the second being a DVD of a live show that we played in San Francisco.

But a year later, the entire project was postponed indefinitely. Andrew from Orange Twin replied to an email from Dan at the Sashwap fansite, basically saying that Jeff decided he didn't like any of the tracks, and shot down the project completely. Perhaps someday they'll convince him to give the go-ahead to release rarities and/or reissue early self-released material. But until Jeff changes his mind, don't expect that stuff to see official release.

In 2005, In The Aeroplane Over The Sea was reissued in the UK. The person at the label overseeing it had tried to get Jeff to approve some unreleased tracks for a bonus disc. But it was to no avail, and the reissue ultimately consisted of only the original album in a special case.

More recently, On Avery Island was slated to have a UK reissue on a different label-- announced in 2006, supposedly a "redux" edition with live and rare bonus tracks. The label went as far as to claim the band themselves were overseeing the project. Delays regarding the bonus tracks supposedly caused the release to be pushed back several times. It wasn't until 2009 that the reissue finally came out, and sadly, the only bonus tracks included were 2 songs, "Everything Is" and "Snow Song Part One", both of which were already widely available on a single.

What are Neutral Milk Hotel's influences?

Kim Cooper's Aeroplane book also mentions several of NMH's other favorites.

Jeremy Barnes is a big fan of Taraf de Ha�douks. Julian Koster loves Lincoln by They Might Be Giants.

But the band would likely site their friends as their biggest influence, such as their fellow Elephant Six artists.