$SPX is the S&P 500. It represents the largest 500 companies in the US, out of more than 4000 public companies actively traded in the exchanges. There are another 15,000 bitty companies near-death that most people do not touch.
$INDU is the Dow Jones Industrial Average (DJIA), or the Dow 30. It consists of 30 companies of various industries (banking, manufacturing, retail, etc...) traded on the NY Stock Exchange, and chosen by a committee from a company that used to be McGraw Hill Financial.
$NDX is the Nasdaq 100 Index. It consists of 100 largest companies listed on the Nasdaq Exchange, which traditionally has been the exchange of choice for technology companies.
All 3 are referenced in the media. The DJIA may not represent the real market because it has only 30 companies, but people are most familiar with it due to its longevity, ever since it was invented by Mr. Dow back in late 19-th century.
All 3 indices are often revised and the constituents changed if a company or industry loses its importance. Of course a change in the Dow 30 is more important because the index has so few companies. Still, the choice of the 30 companies is good enough that the DJIA tracks the S&P 500 fairly well.
The Nasdaq being mostly technology companies represents high tech industries. It has more volatility than the S&P and the Dow. In bullish times, it goes up more, and in bad times it goes down more. So, people like to look at it to feel where the market is going.
The Nasdaq and the Dow constituents do not overlap because they are traded on different exchanges. The S&P has both, so is a broader measure.
PS. Oops. The Nasdaq most often quoted is really $COMPQ, which is all of the companies traded on Nasdaq Exchange. NDX is a subset of COMPQ.
PPS. I should have provided a list of Web pages that describe all this more accurately than from my memory.
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