The aspiring amateur sleuth has plenty of resources for learning how to analyze crime or investigate unsolved cases.
There are several free, in-person ways to learn more about law enforcement and crime. Most of the academies below don't require you to be a resident of their jurisdiction but some do. Nearly all require a background check prior to enrollment.
You can also find criminology books in most academic and public libraries in the following call number ranges:
Dewey - 364
LC System - HV 6001-7220.5
These articles are good places to begin learning the fundamentals of crime analysis and profiling based on offender behavior:
Andresen, Martin A, Richard Frank, and Marcus Felson. “Age and the Distance to Crime.” Criminology & criminal justice 14.3 (2014): 314–333. Print.
Andresen, Martin A., and Jen-Li Shen. “Journey to Crime: How Far Does the Criminal Travel?” CrimRxiv (2019): CrimRxiv, 2019-08. Print.
Godwin, Maurice, and David Canter. “Encounter and Death: The Spatial Behavior of US Serial Killers.” Policing : an international journal of police strategies & management 20.1 (1997): 24–38. Print.
Johnson, Shane D. “How Do Offenders Choose Where to Offend? Perspectives from Animal Foraging.” Legal and criminological psychology 19.2 (2014): 193–210. Print.
Keppel, RD, and JG Weis. “Time and Distance as Solvability Factors in Murder Cases.” Journal of forensic sciences 39.2 (1994): 386–401. Print.
Leong, Kelvin, and Anna Sung. "A review of spatio-temporal pattern analysis approaches on crime analysis." International E-Journal of Criminal Sciences 9 (2015). Online.
Luo, Fei, Yan Zhang, and Larry T. Hoover. “The Journey to Crime and Victimization.” International journal of police science & management 23.3 (2021): 211–221. Print.
Ratcliffe, Jerry H. “The Hotspot Matrix: A Framework for the Spatio-Temporal Targeting of Crime Reduction.” Police practice & research 5.1 (2004): 5–23. Print.
Snook, Brent et al. “Serial Murderers' Spatial Decisions: Factors That Influence Crime Location Choice.” Journal of investigative psychology and offender profiling 2.3 (2005): 147–164. Print.