Useful links to monitoring and troubleshooting SharePoint Server 2013

Understanding the Logging Database
How to Query the WSS_Logging Database
How to Reduce the Size of the Logging Database
SEO in SharePoint Server 2013
SharePoint 2013 Analytics a Big Step Backward
How to Query the WSS_Logging Database
Install SSRS in SharePoint Mode
New-SPUsageApplication
Demystifying SharePoint Performance Management
Capturing Performance Counters for SharePoint
Enabling Usage Reports
SharePoint Usage Reports are Empty
Empty Usage Reports
View Popularity Trends and Most Popular Items
Planning for monitoring in SharePoint 2013
Microsoft Troubleshooting Methodology
Split-Half  Troubleshooting
Deductive Reasoning vs. Inductive Reasoning
SharePoint Farm Documentation Scripts at Codeplex.com
Acceleratio Documentation Toolkit for SharePoint
TechNet SharePoint Updates Center
Stefan Goßner's Blog
Difference between CU, PU, and service packs
How to find your SharePoint version with PowerShell
Software Updates Overview for SharePoint 2013
Farm Patching Explained
Be careful-some patches are on Windows Update
Communications Protocol (Wikipedia)
SharePoint Ports and Protocols
Using IIS Request Tracing
Enable the Developer Dashboard
SharePoint 2013 Troubleshooting Guide
SharePoint 2013 Administration Inside Out
Microsoft Message Analyzer
Microsoft Message Analyzer Operating Guide
Wireshark
Fiddler
Decrypting SSL Traffic with Wireshark
Webalizer
SharePoint Manager 2013
FeatureAdmin for SharePoint 2013
How to Use Kerbtray