Final answer:
The corrected sentence is 'This is the most complete book on English grammar.' with proper superlative form and capitalization.
Step-by-step explanation:
The sentence 'This is the completest book on english Grammar' should be corrected to 'This is the most complete book on English grammar.' The superlative form 'completest' is not standard; the correct superlative form is 'most complete'. Additionally, 'English' should be capitalized as it is a proper noun, and 'grammar' should be written with a lowercase 'g' unless it is the first word in a sentence or part of a title.