Two options, both using free tools from Microsoft:
Option 1. Dumpbin [a console application]
dumpbin.exe /exports c:\windows\system32\user32.dll
Microsoft (R) COFF/PE Dumper Version 14.10.25019.0
Copyright (C) Microsoft Corporation. All rights reserved.
Dump of file c:\windows\system32\user32.dll
File Type: DLL
Section contains the following exports for USER32.dll
00000000 characteristics
584A6BB5 time date stamp Fri Dec 9 03:30:45 2016
0.00 version
1502 ordinal base
1207 number of functions
951 number of names
ordinal hint RVA name
1503 0 0008B620 ActivateKeyboardLayout
1504 1 0002C5A0 AddClipboardFormatListener
1505 2 000937A0 AdjustWindowRect
1506 3 000172C0 AdjustWindowRectEx
1507 4 00015AB0 AdjustWindowRectExForDpi
1508 5 00098340 AlignRects
1509 6 00093800 AllowForegroundActivation
1510 7 0002AC60 AllowSetForegroundWindow
1511 8 0008FCC0 AnimateWindow
...
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Option 2. Dependency Walker [a GUI application]
To load a DLL, you can use either File ... Open, or configure depends.exe to add "View Dependencies" to the context menu for DLL files in explorer.
To configure the context menu:
Exports for user32.dll
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Options ... Configure Handled File Extensions
Add DLL