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Hope Credit and the Lifetime Learning Credit are the two education tax credits available for the "qualified tuition and related expenses" for an "eligible student".

The qualified tuition and related expenses are tuition and fees required for enrollment or attendance at an accredited college, university, vocational school, or other post–secondary educational institution that is eligible to participate in a student aid program administered by the Department
of Education.

An "eligible student" critieria is different for Hope Credit and the Lifetime Learning Credit. Hope credit is available for the first two years of post–secondary education. The Student need to enroll in a degree, certificate, or other recognized educational credential program and is taking at least one–half of the normal full–time workload. The Lifetime Learning Credit can claimed for any student taking course work in order to acquire or improve job skills and can be claimed for any number of years.

The credit is limited by your modified adjusted gross income (modified AGI) and filing status. You cannot claim either credit if you are married filing a separate return.

Books are virtually never allowed as education expenses in arriving at
the allowable Hope Credit. Books are allowed only when they are
required to be purchased from that educational instituion as a condition
of ENROLLMENT or ATTENDENCE. Almost NO educational institutions
impose those conditions.

My wife is taking an online credit course (chemistry) from Iowa community college, and professor asked her to buy one particular book as the course is based on that book. But, buying this books was not
pre-requisit to join the course. Will this book qualify ?

I would say that the book does not qualify as an educational expense
since it was not a requirement of enrollment.