Chapter 1. Introduction.- Chapter 2. Half-Discrete Hardy-Hilbert's Inequalities with Two Internal Variables.- Chapter 3. Half-Discrete Hardy-Hilbert's Inequalities Involving One Upper LimitFunction.- Chapter 4. Half-Discrete Hardy-Hilbert's Inequalities Involving One Derivative Function.

- Chapter 5. Half-Discrete Hardy-Hilbert's Inequalities Involving One Multiple Upper LimitFunction.- Chapter 6. Half-Discrete Hardy-Hilbert's Inequalities Involving One Derivative Functionof Higher-Order.- Chapter 7. Half-Discrete Hardy-Hilbert's Inequalities Involving One Upper Limit Function and One Partial Sum.- Chapter 8. Half-Discrete Hardy-Hilbert's Inequalities Involving One Derivative Functionand One Partial Sum.

- Chapter 9. Half-Discrete Hardy-Hilbert's Inequalities Involving One Multiple Upper Limit Function and One Partial Sum.- Chapter 10. Half-Discrete Hardy-Hilbert's Inequalities Involving One Derivative Functionof Higher-Order and One Partial Sum.