How can I get html elements classes inside Angular Component?

If you are asking for just getting and settings classes from any HTML elements like div etc. you can use ElmentRef in angular.

You can use template variable (i.e. #useThisTemplateVar) to get HTML element and simply target that element with @ViewChild() decorator.

import { Component, ElementRef, ViewChild } from "@angular/core";

@Component({
  selector: "app-example",
  template: `

 <div #useThisTemplateVar class="myClass">
   My some other content!
 </div>

<button type="button" (click)="changeClass()">change class</button>

`,
  styleUrls: ["./example.component.scss"]
})

export class ExampleComponent implements {

@ViewChild('useThisTemplateVar') elRef: ElementRef; 
changeClass(): void {
  this.elRef.nativeElement.className === "myClass" ? 
  this.elRef.nativeElement.className = "yourClass" : 
  this.elRef.nativeElement.className = "myClass"; 
}

}

Note: As per angular Security guide you should stop using direct access to DOM elements to prevent XSS attacks to your Web Application.

Learn More: ElementRef Angular official documentation, Angular security Guide