I am currently delving into the Large Sieve Inequality, consulting Chapter 27 of Davenport's Multiplicative Number Theory. Having completed the chapter, I seek a deeper understanding of the practical applications of the Large Sieve Inequality to enhance my comfort and satisfy my curiosity. I would greatly appreciate it if someone could provide statements related to the Large Sieve Inequality along with references, without the need for detailed proof explanations. Additionally, I am interested in exploring simple applications, such as determining the count of perfect squares in $[1, N]$, the number of primes in $[M+1, M+N]$, and the count of twin primes in $[1, N]$. These basic applications will help solidify my comprehension.
Furthermore, I have come across mentions of an application of the Large Sieve Inequality for estimating the sum $d(p-1)$, where the sum varies for primes less than or equal to $x$. Despite diligent searching over the past few days, I have been unable to find a suitable reference for this specific application. Any guidance or reference regarding this matter would be greatly appreciated.