It looks like you're interested in "The Cat Who" book series and want to know the order of the books. Here's a list of the books in the series by Lilian Jackson Braun, in the order they were published:
The Cat Who Series by Lilian Jackson Braun – Reading Order
- The Cat Who Could Read Backwards (1966)
- The Cat Who Ate Danish Modern (1967)
- The Cat Who Turned On and Off (1968)
- The Cat Who Saw Red (1986)
- The Cat Who Played Brahms (1987)
- The Cat Who Played Post Office (1987)
- The Cat Who Knew Shakespeare (1988)
- The Cat Who Sniffed Glue (1988)
- The Cat Who Went Underground (1989)
- The Cat Who Talked to Ghosts (1990)
- The Cat Who Lived High (1990)
- The Cat Who Knew a Cardinal (1991)
- The Cat Who Moved a Mountain (1992)
- The Cat Who Wasn't There (1992)
- The Cat Who Went up the Creek (1993)
- The Cat Who Brought Down the House (1994)
- The Cat Who Talked Turkey (1996)
- The Cat Who Went Bananas (1997)
- The Cat Who Dropped a Bombshell (1998)
- The Cat Who Said Cheese (1999)
- The Cat Who Tailed a Thief (2000)
- The Cat Who Sang for the Birds (2001)
- The Cat Who Saw Stars (2002)
- The Cat Who Robbed a Bank (2004)
- The Cat Who Smelled a Rat (2005)
- The Cat Who Went into the Closet (2006)
- The Cat Who Came to Breakfast (2007)
- The Cat Who Blew the Whistle (2009)
- The Cat Who Had 60 Whiskers (2011)
If you want, I can help you find summaries or recommendations on where to start! Would you like that?