Genesis 1:25-26 – God seemingly created first the animals and afterwards He created man
Genesis 2:18-19 – God seems to have created man first and afterwards He created the animals
This actually is a point often mentioned as a "contradiction" by critics of the Bible, and indeed on just cursory reading of the record one could perhaps get the impression as if there was a different sequence given about the creation of man and animals. But, a closer look at these verses and observing the context of the chapters as a whole will show that there really is not a contradiction, rather the records complement each other in a harmonious way.
The record in Genesis 1 actually to Genesis 2:4 forms the first major section of the book, and it gives the details about God's working when restoring the heavens and the earth in a chronological manner. From Gen 2:5 onward, the record actually goes back in time and fills in certain details about that which was handled only briefly in the previous chapter. The sequence is according to subject matter rather than being chronological.
The difficulties arise when it is not recognized that the record in Gen 2 doesn't claim to be a chronological record about what happened ... only when read as if it were a chronologically arranged record do the problems arise. God of course is not bound to always use a chronological sequence to events, and it must be understood that at times He gives further details about previously mentioned events in a manner which is ordered by the contents or the subjects. The record in Gen 2:15ff tells us some more about the making and creation of man, and how man was put in the garden of God, etc. Various details are then given about what happened in the garden, how man lived in fellowship with God and how he walked with God. But, these verses do not even say that animals were created after man, there really is not a mention about the time sequence. The creation of the animals is not mentioned, rather certain things which happened with the animals which already had been created.
Careful reading and observing the overall context of the passages in question helps determine the solution to this apparent contradiction.