npm no longer installs peer dependencies so you need to install them manually, just do an npm install on the needed deps, and then try to install the main one again.
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it’s right in that message, it says which deps you’re missing
UNMET PEER DEPENDENCY angular-animate@^1.5.0 +--
UNMET PEER DEPENDENCY angular-aria@^1.5.0 +-- angular-material@1.0.6 +
UNMET PEER DEPENDENCY angular-messages@^1.5.0 `-- mdi@1.4.57`
So you need to npm install angular angular-animate angular-aria angular-material angular-messages mdi