Why is M0 higher than M1? In my understanding, M2 includes M1 and M1 include M0. However, I checked the money supply here and used the "Compare" function to compare the money supply of m0 with money supply of m1, and found that the money supply of M0 is higher than that of M1. How come?
Because what Trading Economics states to be M0 is not really M0 but the monetary base (MB). Compare the data in their graph with the data from the Fed (e.g. here). These are some of the values from the monetary base (variable BOGMBASE):

2016-09-01  3735888
2016-10-01  3572132
2016-11-01  3629770
2016-12-01  3531565
2017-01-01  3595455
2017-02-01  3746401
2017-03-01  3856260
2017-04-01  3821654
2017-05-01  3774390


They correspond roughly to the ones in the TE graph.

Whilst M1 is indeed larger than M1, the monetary base does not need to be. This is the entry in the Wikipedia article for monetary supply in the US:


M0: The total of all physical currency including coinage. M0 = Federal Reserve Notes + US Notes + Coins. It is not relevant whether the currency is held inside or outside of the private banking system as reserves.
MB: The total of all physical currency plus Federal Reserve Deposits (special deposits that only banks can have at the Fed). MB = Coins + US Notes + Federal Reserve Notes + Federal Reserve Deposits
M1: The total amount of M0 (cash/coin) outside of the private banking system plus the amount of demand deposits, travelers checks and other checkable deposits


A similar entry from the Fed website indicates that M1 does not include the whole of MB. The relevant quote is:


  The monetary base is defined as the sum of currency in circulation and reserve balances (deposits held by banks and other depository institutions in their accounts at the Federal Reserve). M1 is defined as the sum of currency held by the public and transaction deposits at depository institutions (which are financial institutions that obtain their funds mainly through deposits from the public, such as commercial banks, savings and loan associations, savings banks, and credit unions).


It follows that the data from Trading Economics is misleading. It might be worth pointing this out to them.