What software can I use to read png metadata?

Using ImageMagick:

identify -verbose image.png

ImageMagick should be cross-platform. I tried it on Linux with your attached image:

[...]
Properties:
  Author: Hans Müller
  Date: 2010-12-08 09:45
  date:create: 2010-12-08T13:15:43+01:00
  date:modify: 2010-12-08T13:15:43+01:00
  Desc: A long time ago in a galaxy far far away....
  signature: 3b4a54202316a7ae4b4fe0e431d47958181f4bb893493355820d4ba74f9f5ee3
[...]

Another option is TweakPNG, on Windows.

I can see that is having problems displaying the Hans Müller name in your image, so maybe it does not work with Unicode metadata.

If you are looking for a PNG-only solution, try pngchunks:

$ sudo apt-get install pngtools
$ pngchunks UiagX.png
Chunk: Data Length 13 (max 2147483647), Type 1380206665 [IHDR]
  Critical, public, PNG 1.2 compliant, unsafe to copy
  IHDR Width: 800
  IHDR Height: 600
  IHDR Bitdepth: 8
  IHDR Colortype: 2
  IHDR Compression: 0
  IHDR Filter: 0
  IHDR Interlace: 0
  IHDR Compression algorithm is Deflate
  IHDR Filter method is type zero (None, Sub, Up, Average, Paeth)
  IHDR Interlacing is disabled
  Chunk CRC: 353637671
Chunk: Data Length 9 (max 2147483647), Type 1935231088 [pHYs]
  Ancillary, public, PNG 1.2 compliant, safe to copy
  ... Unknown chunk type
  Chunk CRC: 10132504
Chunk: Data Length 19 (max 2147483647), Type 1951942004 [tEXt]
  Ancillary, public, PNG 1.2 compliant, safe to copy
  ... Unknown chunk type
  Chunk CRC: -1325924661
Chunk: Data Length 21 (max 2147483647), Type 1951942004 [tEXt]
  Ancillary, public, PNG 1.2 compliant, safe to copy
  ... Unknown chunk type
  Chunk CRC: 134517081
Chunk: Data Length 58 (max 2147483647), Type 1951945850 [zTXt]
  Ancillary, public, PNG 1.2 compliant, safe to copy
  ... Unknown chunk type
  Chunk CRC: 1701487776
Chunk: Data Length 572939 (max 2147483647), Type 1413563465 [IDAT]
  Critical, public, PNG 1.2 compliant, unsafe to copy
  IDAT contains image data
  Chunk CRC: 1174233759
Chunk: Data Length 0 (max 2147483647), Type 1145980233 [IEND]
  Critical, public, PNG 1.2 compliant, unsafe to copy
  IEND contains no data
  Chunk CRC: -1371381630

The output of pnginfo may not verbose enough for your usage:

$ pnginfo UiagX.png
UiagX.png...
  Image Width: 800 Image Length: 600
  Bitdepth (Bits/Sample): 8
  Channels (Samples/Pixel): 3
  Pixel depth (Pixel Depth): 24
  Colour Type (Photometric Interpretation): RGB 
  Image filter: Single row per byte filter 
  Interlacing: No interlacing 
  Compression Scheme: Deflate method 8, 32k window
  Resolution: 2835, 2835 (pixels per meter)
  FillOrder: msb-to-lsb
  Byte Order: Network (Big Endian)
  Number of text strings: 3 of 9
    Author (tEXt uncompressed): Hans Müller
    Date (tEXt uncompressed): 2010-12-08 09:45
    Desc (tEXt uncompressed): A long time ago in a galaxy far far away....