Some of the most important tools for Search Engine Optimization are actually… from Google itself. Whether it is about page speed, identify new keywords, here a few tools:
Google Keyword Planner
really useful and free, highly recommended, my favourite.
https://adwords.google.com/KeywordPlanner
Google Trends
https://trends.google.com/trends/
Google Rich Results Test
https://search.google.com/test/rich-results
Google Page Speed
https://developers.google.com/speed/pagespeed/insights/
Google Search Console
https://search.google.com/search-console
Outside of the Google universe, many other good resources available:
MOZ Link Explorer
https://moz.com/link-explorer
10 analysis for free per month. What I especially like: link intersect, helps you identify which website links to your competitors but not to you.
Reddit Keyworddit
https://www.highervisibility.com/free-seo-tools/keyworddit/
Answer the public
nice tool, but very limited use and super expensive: 2 searches are free, after that you have to pay a 99€ per month subscription. Crazy.
https://answerthepublic.com/
KParser
https://www.kparser.com/
Timo Specht
https://www.timospecht.de/
Screaming Frog
https://www.screamingfrog.co.uk/seo-spider/
SEMRush Website Penalty Indicator
https://feinternational.com/website-penalty-indicator
SEMRush
https://www.semrush.com
SEO Surfer
https://surferseo.com/