Few American companies evoke more complicated feelings than our largest automaker, General Motors (NYSE: GM). Once the no-brainer largest car company in the world, with half of the U.S. market, GM was in decline for decades as quality diminished and imported brands claimed much of its home market.

That decline cost it a lot of goodwill, but much more was lost (in some circles, at least) after GM received a government bailout in 2009 that was seen as favoring the company's unions as the expense of its bondholders. Since then, the General has become something of a "political punching bag," in its CEO's words, and it has struggled to make its message heard.

But the political hot air might be obscuring a big story: GM is in the midst of a dramatic renaissance – one that hasn't yet been reflected in the company's surprisingly low share price. Here are three reasons to take a closer look at buying stock in the General.

Reason No. 1: The cars are getting good
Here's an investment tip: Want to evaluate an automaker's stock prospects? Start by driving its cars. An automaker with great, class-leading products will be able to command premium prices, which should lead to healthy margins and strong earnings. On the other hand, an automaker with mediocre products will have to discount its cars and trucks to keep sales going, and its margins and profits will suffer over time.

GM was the king of the discounters for years, but that is slowly starting to change. While the automaker's incentives -- the industry term for those "cash back" or discounted-financing offers you see advertised -- remain among the highest in the U.S. market, its newest models are solidly competitive and selling well without heavy discounts.

Those models include several excellent small cars: the Chevy Cruze compact, which saw sales jump last year when Toyota (NYSE: TM) was short of its class-leading Corollas; the Chevy Sonic subcompact, which is outselling Ford's (NYSE: F) critically acclaimed Fiesta; and the Buick Verano, a luxurious made-in-Michigan variant of the German-engineered Opel Astra.  All saw solid sales as gas prices rose earlier this year: For the first time in a long time, maybe ever, GM has several fuel-efficient small cars that compare well with Toyota and Honda (NYSE: HMC).

That said, GM's product line is still very much a work in progress. Key new-vehicle programs were delayed or halted during GM's long slide into bankruptcy, and it will be another year or two before the General's U.S. lineup can match the end-to-end excellence of Ford's. But for investors, that's the opportunity: The high quality of GM's recent models suggest that its forthcoming models will also be very competitive, and GM's margins and profits should continue to improve as those vehicles arrive at dealers.

Reason No. 2: Strong profits are poised to get stronger
Last year was the most profitable in GM's history – but CEO Dan Akerson isn't satisfied. In a nutshell, Akerson thinks a company the size of GM should be making significantly more money, and he's determined to bring that about.

A closer look at the numbers suggests that GM does in fact have plenty of opportunities for improvement. Consider that $1.7 billion of GM's $2.2 billion in pretax profits in the first quarter were attributable to its North American region, nearly all of that amount coming from the United States. Improvements to profitability overseas and reductions in incentives spending here at home will both boost profits significantly -- as will further reductions in GM's bloated marketing and product-development costs.

The good news for investors: All of those things are actually happening, thanks to Akerson and his core team of (very capable) executives. GM's profit growth should outpace its sales growth significantly over the next few years.

Reason No. 3: Small signs of progress are adding up
When viewed as a whole, GM's global lineup of vehicles is duplicative and somewhat poorly thought out. A comprehensive plan has been put in motion to change that by 2018. GM's product-development process has long been prone to delays and expensive last-minute changes. That has been addressed, saving more than $1 billion a year. GM's global pension liability is huge, big enough to nearly wipe out the company's $30 billion-plus cash hoard. Stealing a page from Ford, CFO Dan Ammann just addressed a big part of it -- and set the stage for a solution to the company's U.S. hourly pension-plan liability, far and away its biggest.

You get the idea: Slowly but surely, GM's remaining chronic problems are being addressed in smart ways by new leaders with track records of success. Some of those problems, like restructuring GM's money-torching European division, might take years to solve -- but already, solutions have been set in motion.  As those solutions bear fruit in coming months and years, GM's profits -- and share price -- should trend solidly upward.

The upshot: a company on the upswing, selling for cheap
GM is selling for about 6.5 times earnings as I write this, well below the average historical multiple (around 10) seen on healthy automakers. There's no question that GM's well out of danger -- it led the world in sales last year and generated record profits -- but there's also no question that considerable room for improvement remains.

The case for buying GM boils down to this: After decades of intransigence, those improvements are actually happening. GM's lingering problems -- and its sullied reputation -- have kept its share price down. But as those problems are solved, and as its much-improved products help heal its reputation, shareholders are likely to be rewarded.

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This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.