Gautam Adani, an Indian businessman, is one of the richest people in the world. His wealth took a big hit when shares of companies owned by his flagship Adani Group fell dramatically following the publication of a report by a U.S. short seller in late January. Here is what you need to know about the Adani saga.

The Adani Group is big—and politically connected.

There are seven India-listed companies bearing the Adani name, including firms in power transmission, green energy and port operation. Adani Group also owns cement producers, airport operators, coal miners and a digital marketing company.

That has made Mr. Adani, the founder of the group, one of the richest men in the world. He briefly surpassed Jeff Bezos on the Bloomberg Billionaires Index in September 2022. Mr. Adani has lost around 40% of his net worth since the release of the report by Hindenburg Research, according to the index, which said he was worth around $72.1 billion on Feb. 2.

Mr. Adani has ties to Narendra Modi, India’s prime minister. The two men were both born in the state of Gujarat and it is where Mr. Modi first rose to political prominence and Mr. Adani began building his business empire.

When Mr. Modi was chief minister of Gujarat, the government sold its stake in a port joint venture to Adani Exports. It became India’s largest private port, giving a key business success to Mr. Adani—and an important political win to Mr. Modi.

Hindenburg accused the company of fraud.

Nathan Anderson, founder of Hindenburg Research, released a report on Jan. 24 accusing the Adani Group of “brazen stock manipulation and accounting fraud.”

Hindenburg seeks out companies that it believes have lied about their business or misled investors. Its most high-profile success was Nikola Corp., whose shares had soared on promises it would produce electric and hydrogen-powered trucks. 

Mr. Anderson and his staff produce detailed reports that feature on-the-ground digging in an attempt to prove their claims. Their smoking gun on Nikola was a video of one of the company’s trucks zooming down the highway. They showed that the truck was actually rolling downhill and not running on its own power. 

Mr. Anderson claimed the Adani Group uses a number of shell companies to inflate stock prices and flout India’s shareholding rules, which require at least 25% of most listed companies to be held by the public. 

He also raised more general questions about Adani’s business model, pointing to the group’s heavy debt burden and elevated share prices. Some of these points have been made before by others. In August, debt-research firm CreditSights called the Adani Group “deeply overleveraged.”

On Jan. 27, Adani published a 413-page rebuttal, calling Mr. Anderson’s company “the Madoffs of Manhattan,” a reference to Ponzi schemer Bernard Madoff. Adani said it provided an answer to each of Hindenburg’s points. Hindenburg has since issued a response to the group’s rebuttal.

Adani Group share prices have dived.

The initial market response to the Hindenburg report was relatively subdued. Although the share price of Adani Total Gas Ltd.

fell by around 5.6% on Jan. 25, other Adani companies performed much better. Adani Enterprises Ltd., the group’s flagship company, fell by around 1.5%, in line with the wider market.

The mood changed quickly within days. On Jan. 27, Adani Enterprises closed down 18.5%. Other companies hit the 20% limit allowed for their shares by India’s exchanges. The shares have continued to slide and by Thursday they had collectively lost more than $100 billion of value.

Why the abrupt change? It can sometimes take markets some time to review and digest lengthy short seller reports, which have had a mixed record and aren’t always taken seriously. But Adani may have also drawn attention to the accusations with its responses, which included calling Hindenburg’s claims “nothing but a lie” and saying they had “led to unwanted anguish for Indian citizens.” 

Adani Enterprises failed to sell new shares in a closely watched offering.

This was all happening at the same time Adani Enterprises was preparing for a large share sale that was meant to raise more than $2 billion. The public offering had been scheduled to wrap up on Jan. 31.

The share sale emerged as a test of Mr. Adani’s ability to raise capital and fend off the allegations by Hindenburg

Before the Hindenburg report, the shares were being offered at a discount to the market price. But after the report caused a deep selloff, the shares fell below the offering price. 

Nevertheless, Adani Enterprises pushed ahead with the offering and a last-minute flurry of investor bids enabled the deal to be fully subscribed. The deal was helped along by a commitment from International Holding Co. PJSC, an Abu Dhabi-based company that previously invested in Adani companies.

The day after subscriptions closed, shares of Adani Enterprises fell 28%, meaning the buyers of the offering would incur big losses if the deal went through. Adani canceled the sale late on Feb. 1. 

Adani companies are due to release their earnings reports soon.

The listed companies in the Adani Group will soon report their earnings for October through December 2022, the third quarter of India’s financial year. 

That will give them a chance to win over investors who have become skeptical in the wake of the Hindenburg report—but it may prove difficult. Among Mr. Anderson’s claims is the suggestion that Adani companies use shell corporations to manipulate their earnings. The Indian conglomerate has denied any wrongdoing.

This explanatory article may be periodically updated.

Write to Matthew Thomas at matthew.thomas@wsj.com