This course will mainly focus on potential quantum computing algorithms and applications for noisy intermediate-scale quantum (NISQ) machines. After decades of efforts in constructing practical quantum computers, we are now in the so-called NISQ era without quantum error correction. It may still be a long way to go to realize a fully-functional error-corrected quantum computer. Thus it is important to find quantum algorithms that can achieve significant advantages or speedups for important problems with substantial sizes already hard for classical computation and yet just use the NISQ devices with imperfect gates. So in this course, we will introduce hybrid quantum-classical variational algorithms that leverage the strengths of both quantum and classical computation. In particular, we will investigate potential quantum computing applications in quantum computational chemistry, quantum machine learning, and quantum optimization using these algorithms.